Equipment fitting system that compares swing metrics

ABSTRACT

An equipment fitting system that measures swings by a user of different pieces of equipment with inertial sensors, and analyzes sensor data to recommend which piece of equipment is optimal for the user from among those tested. Illustrative applications include fitting of baseball bats and golf clubs. Swing metrics calculated from sensor data may include an acceleration metric, a speed metric, and a momentum metric; these metrics may be combined into a metrics score for each piece of equipment. Other factors may be included in an overall score, such as the user&#39;s subjective score for each piece of equipment, and ratings from experts or other consumers. Users may assign the relative importance for the different factors to calculate an overall equipment score.

This application is a continuation-in-part of U.S. Utility patentapplication Ser. No. 17/359,407, filed 25 Jun. 2021, which is acontinuation-in-part of U.S. Utility patent application Ser. No.17/228,635, filed 12 Apr. 2021, which is a continuation of U.S. Utilitypatent application Ser. No. 16/835,247, filed 30 Mar. 2020, issued asU.S. Pat. No. 10,974,121 on 13 Apr. 2021, which is acontinuation-in-part of U.S. Utility patent application Ser. No.16/189,889, filed 13 Nov. 2018, which is a continuation of U.S. Utilitypatent application Ser. No. 15/628,613, filed 20 Jun. 2017, issued asU.S. Pat. No. 10,124,230, which is a continuation-in-part of U.S.Utility patent application Ser. No. 15/214,339, filed 19 Jul. 2016,issued as U.S. Pat. No. 9,694,267, the specifications of which arehereby incorporated herein by reference.

This application is also a continuation-in-part of U.S. Utility patentapplication Ser. No. 17/359,407, filed 25 Jun. 2021, which is acontinuation-in-part of U.S. Utility patent application Ser. No.17/228,635, filed 12 Apr. 2021, which is a continuation of U.S. Utilitypatent application Ser. No. 16/835,247, filed 30 Mar. 2020, issued asU.S. Pat. No. 10,974,121 on 13 Apr. 2021, which is also acontinuation-in-part of U.S. Utility patent application Ser. No.16/166,490, filed 22 Oct. 2018, which is a continuation of U.S. Utilitypatent application Ser. No. 15/590,398, filed 9 May 2017, issued as U.S.Pat. No. 10,109,061 which is a continuation of U.S. Utility patentapplication Ser. No. 15/087,776, filed 31 Mar. 2016, issued as U.S. Pat.No. 9,646,199, which is a continuation in part of U.S. Utility patentapplication Ser. No. 14/801,568, filed 16 Jul. 2015, issued as U.S. Pat.No. 9,396,385, the specifications of which are hereby incorporatedherein by reference.

This application is also a continuation-in-part of U.S. Utility patentapplication Ser. No. 17/359,407, filed 25 Jun. 2021, which is acontinuation-in-part of U.S. Utility patent application Ser. No.17/228,635, filed 12 Apr. 2021, which is a continuation of U.S. Utilitypatent application Ser. No. 16/835,247, filed 30 Mar. 2020, issued asU.S. Pat. No. 10,974,121 on 13 Apr. 2021, which is also acontinuation-in-part of U.S. Utility patent application Ser. No.16/181,955, filed 6 Nov. 2018, which is a continuation of U.S. Utilitypatent application Ser. No. 15/815,571, filed 16 Nov. 2017, issued asU.S. Pat. No. 10,121,066, the specifications of which are herebyincorporated herein by reference.

BACKGROUND OF THE INVENTION Field of the Invention

One or more embodiments setting forth the ideas described throughoutthis disclosure pertain to the field of motion capture sensors andanalysis of motion capture data. More particularly, but not by way oflimitation, one or more aspects of the invention enable an equipmentfitting system that compares swing metrics.

Description of the Related Art

Methods for analyzing swings of a piece of equipment, such as a golfclub, tennis racquet or baseball swings for example include videocapture systems that record high speed video of a swing and that analyzethe motion of the piece of equipment, club, racquet or bat, etc., andthe player from the video. These systems are typically expensive andcomplex, and they are not portable. Another method is to attach a motionsensor to the piece of equipment, e.g., a bat, etc., and to analyzemotion data captured by the sensor during the swing. A significantchallenge for these sensor based solutions is interpretation of thesensor data. In particular, sensors typically capture data in a localreference frame defined by the sensor geometry. This sensor referenceframe moves and rotates constantly throughout a swing. For example, fora baseball bat, this challenge is more complex since the bat hasrotational symmetry around its long axis; thus the batter can hold thebat in multiple orientations while swinging, which changes the sensordata. This applies to other sports that involve a swing of a piece ofequipment and any discussion oriented towards a bat herein is notlimiting, and can be applied to any other type of equipment thatinvolves a swing as well. There are no known methods that transformswing sensor data from a sensor based reference frame to a meaningfulreference frame that is insensitive to these changes in orientation.Existing methods emphasize vector magnitudes (such as total swing speed)in defining swing metrics because these magnitudes are invariant torotations in the sensor reference frame. However, individual componentsof sensor measurements along carefully chosen transformed axes providemore detailed and more physically meaningful information.

In baseball and related sports, the trajectory of specific point on thebat or other piece of equipment, for example the sweet spot, is ofparticular importance since this is the optimum location on the bat forstriking the ball. There are no known methods that combine analysis ofthe sweet spot trajectory with a swing plane reference frame.

Another limitation of existing methods for analyzing swings is that thequantities measured and reported cannot be easily correlated to swingmechanics or to the factors that make for efficient and effectiveswings.

There are no known systems that analyze motion data from sensors to makeequipment recommendations, or that capture sensor data while users aretrying different pieces of equipment and analyze this data to determinewhich piece of equipment is optimal for the user.

For at least the limitations described above there is a need for anequipment fitting system that compares swing metrics.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the invention enable a system to analyze a swing of apiece of equipment, for example a baseball bat, tennis racquet, or golfclub, etc., by transforming sensor data captured during the swing to areference frame that reflects the physics and geometry of the swingitself. This reference frame is called a swing plane reference frame.Metrics defined with respect to the swing plane reference frame providea detailed characterization of a swing; these metrics can be comparedacross swings to analyze the factors that affect swing performance. Forsimplicity, examples directed at baseball bat swings are detailedherein, however, the exemplary embodiments described herein may also beapplied to any other piece of equipment that involves a swing, includingbut not limited to a golf club, tennis racquet, etc.

One or more embodiments of the invention may obtain sensor data from asensor coupled to a bat while the bat is swung to hit or otherwisecontact a ball. The bat may be for example, without limitation, abaseball bat, a softball bat, or a cricket bat. The sensor may forexample be an inertial motion sensor that includes any or all of a threeaxis accelerometer, a three axis gyroscope, and a three axismagnetometer. The sensor may be a compound sensor that incorporatesmultiple individual sensors of any types. A compound sensor may includemultiple sensors at different locations on the bat; for example, withoutlimitation, some sensors may be located on the knob of the bat, andother sensors may be located at the tip of the bat. Sensor data may becollected throughout the swing, for example at a rate of 10 Hz, 100 Hz,1000 Hz, or more. The sensor data may be analyzed to determine the timeof impact between the bat and a ball. For example, accelerometer data,i.e., or acceleration data, may detect the shock of the impact. A battrajectory may be calculated from the sensor data. The trajectory mayinclude motion data samples at multiple points in time throughout theswing; each motion data sample may describe one or more of the bat'sposition, orientation, velocity, angular velocity, acceleration, orangular acceleration at a point in time.

Analysis of the bat trajectory may include calculating an impactvelocity vector for the velocity of the bat at the time of impact withthe ball. Using the impact velocity vector, a reference frame called theswing plane reference frame may be defined for the swing. The swingplane reference frame may be formed from three axes: a first axis may bethe longitudinal axis of the bat; a second axis may be the impactvelocity vector; and a third axis may be orthogonal to the swing planespanned by the first (bat) axis and the second (impact velocity) axis.The angular velocity vector of the bat, which is the rotational axisthat is perpendicular to the bat's instantaneous plane of rotation, mayalso be used to define or calculate one or more of the axes of the swingplane reference frame. The bat trajectory may then be transformed to theswing plane reference frame for further analysis. This analysis mayinclude creating one or more swing metrics from the transformed battrajectory.

Illustrative metrics that may be defined using the transformed battrajectory include the following: Swing plane speed at any point in timeduring the swing may be defined as an instantaneous rotational speed ofthe bat trajectory projected onto the swing plane. In one or moreembodiments, this swing plane speed may be calculated by projectingangular velocity onto the normal vector of the swing plane. Swingduration may then be calculated by defining the start of downswing asthe latest time prior to impact when the swing plane speed has magnitudezero. Subtracting the start of downswing from the time of impactgenerates a duration metric called the time to contact, which measureshow quickly the batter responds. The amount of bat motion may bemeasured as the total angle traversed by the bat both in the swing plane(yielding a metric called total swing angle) and in a plane orthogonalto the swing plane (yielding a different metric called off plane angle).A measure of bat acceleration through the swing may be defined bymeasuring the swing plane speed at the halfway point of a swing; theratio of this halfway point swing plane speed to the peak swing planespeed through the swing is defined as the swing tempo metric.

One or more embodiments may obtain a database of swings from multipleplayers. Analysis of the database may be used to generate one or moreperformance rating functions that rate swings on their relativeperformance. These performance rating functions may be applied to ratefuture swings, and to provide feedback to users on the performance andcharacteristics of their swings. Metrics and other data associated withswings in the database may be combined into feature vectors that may beused for classification and matching algorithms. For example, analysisof the database may be used to group swings into swing styles, whereswings associated with the same swing style have similar featurevectors. Feature vector clustering and matching may be used to providefeedback to a user on the style of his or her swing, and to identifyother users with similar swings. The feature vector may also includeother data related to the swing event, such as for example incomingpitch trajectory or classification, outgoing ball trajectory, or gameoutcome (such as foul, fly-out, home run, etc.) in order to refineclassification and analysis.

In situations where sensor data is unavailable or is saturated at thelimit of the sensor's range for a time interval during a swing, one ormore embodiments may extrapolate sensor data prior to or after theinterval to estimate actual values during this interval. Extrapolationmay for example use a Bézier curve. The curve may be for example a cubicBézier curve with four control points that are selected to match thevalues and the slopes of the sensor data curve at the endpoints of theinterval. One or more embodiments may use a Kalman filter, or a similarstate space estimator, to extrapolate sensor data into the timeinterval. A Kalman filter may for example incorporate a kinematic modelof the bat in order to predict motion parameters when sensor readingsare not able to fully track the motion, for example because the motionis outside the sensor's measurement range.

One or more embodiments of the invention may calculate a trajectory ofthe sweet spot or of a similar or other point on a bat or piece ofequipment, and may derive metrics describing a swing from thistrajectory. The sweet spot trajectory may be calculated from sensordata, for example from a sensor coupled to the bat, which may forexample include accelerometer or gyroscope data. Data may be transformedto a reference frame that may for example be centered at the sweet spotat the time of impact. A reference frame may be defined for example,without limitation, with a z-axis pointing vertically upward, and anx-axis oriented so that the longitudinal axis of the bat is in thexz-plane at impact. The time of impact may be calculated by searchingthe sensor data time series for event signatures that may for examplehave acceleration and angular velocity exceeding respective thresholdvalues. A sweet spot as utilized herein may also indicate a range oflocation or shape of area on the piece of equipment where an impactoccurs or is to occur, wherein the sweet spot meets a predefinedthreshold, or value, for maximum energy transfer, maximum ball speed orleast vibration or any other metric related to efficiency or power forexample, or using any other metric to define the location or range orarea or area range on the piece of equipment.

One or more embodiments may detect a virtual impact for an air swing,when a bat may not physically strike a ball. For example, one or moreembodiments may detect an air swing by determining whether the swing isa valid air swing, and then detecting a point in the swing when angularvelocity in the xy-plane is maximum. A valid air swing may for examplerequire that peak xy angular velocity and peak z-axis accelerationexceed respective threshold values.

One or more embodiments may calculate a start of downswing for a swing,and may calculate a time to contact metric as a difference between thetime of impact and the start of downswing.

One or more embodiments may calculate the trajectory of the position ofthe hands on the bat through the swing. This trajectory may be used forexample to calculate a center of rotation for the swing. For example,the center of rotation may be calculated as a point equidistant from thehand position at three different points on the hand trajectory. An axisof rotation may be calculated as an axis perpendicular to the planethrough these three points. A body tilt angle may be calculated as theangle between the axis of rotation and the vertical direction.

One or more embodiments may calculate and use a two-lever model of theswing, which models the swing mechanics as a body lever extending fromthe center of rotation to the hand position, and a bat lever thatextends from the hand position to the sweet spot. A body ratio metricmay be calculated based on the ratio of the rotation of the body leverthrough the swing to the rotation of the bat lever. The angle betweenthe bat lever and the body lever changes through the swing as the battercocks and then releases the wrist. A hinge angle may be calculatedthrough the swing based on the relative orientation between the batlever and the body lever; for example, the hinge angle may be defined asthe angle between the bat lever and the tangent to the body lever. Thehinge angle at impact may be used as a swing metric.

A commit event may be calculated to reflect when the batter releases thewrist during the swing. For example, the time of commit may becalculated as the time when the angular velocity of the hinge angleexceeds a threshold value. The hinge angle at the time of commit may beused as a swing metric. The hinge release metric may be calculated asthe difference between the hinge angle at impact and the hinge angle atcommit.

One or more embodiments may determine a swing plane for the swing. Theswing plane may be calculated based on the position, orientation, andvelocity of the bat at the time of impact. For example, the swing planemay be a plane through the sweet spot at impact, which is spanned by thebat's longitudinal axis at impact and by the velocity vector of thesweet spot at impact.

At any point in the swing, the distance between the sweet spot and theswing plane may be calculated as an off-plane distance. An on-planeevent may be calculated as the point in the swing when the off-planedistance is within a specified threshold and remains within thisthreshold until impact. An on-plane metric may be calculated as theangular range of motion of the bat or of one or both of the body and batlevers between the on-plane event and the impact event.

The bat forward velocity at any point in time may be calculated as thevelocity of the sweet spot projected onto a plane perpendicular to thelongitudinal axis of the bat. Bat speed at impact may be calculated asthe forward bat speed at the time of impact. A peak bat speed may becalculated as the maximum forward bat speed through the swing. Swingpower may be calculated as a product of the bat speed at impact, themass of the bat, and the average acceleration of the sweet spot duringthe swing.

A swing plane tilt angle metric may be calculated as the angle betweenthe bat's longitudinal axis at impact and the horizontal. An attackangle metric may be calculated as the angle between the sweet spotvelocity vector at impact and the horizontal.

One or more embodiments of the invention may include utilizing sound orat least one Virtual Reality (VR), Augmented Reality (AR) or MixedReality (MR) display, glasses or goggles to provide bio-feedback to theuser. For example, in one or more embodiments, a sound or visual displaymay be utilized to provide feedback to the user to indicate a correctposition, or movement has been achieved. This enables a user to work onportions of a swing or an entire swing using different body positions,for example to simulate different feet positions in a sand trap for agolf swing for example and obtain feedback regarding the position and/orswing using sound or visual feedback. In addition, by providing metricsregarding the body position, body movement, piece of equipment position,piece of equipment movement or any combination thereof, embodiments ofthe invention enable a user to work on developing more power andimproving skills in a bio-feedback environment and/or combineenvironment. Embodiments of the system also enable rehabilitation andgeneral training of the body based on the data gathered by the system tosuggest areas of the body to strength or stretch to improve the range ofmotion to avoid injury through use of correct biomechanics.

One or more embodiments of the invention may include an inertial sensoron or in a bat, and a processor that analyzes data from the inertialsensor to generate one or more swing quality metrics. The processor maybe attached to a memory that contains a bat geometry definition, whichmay for example define a hand position and a sweet spot position alongthe longitudinal axis of the bat. The processor may receive a timeseries of inertial sensor data, including acceleration data from athree-axis accelerometer and angular velocity data from a three-axisgyroscope. It may then calculate the trajectory of the hand position,the trajectory of the sweet spot, and the trajectory of the bat'slongitudinal axis, and the time the bat impacts the ball. From the handtrajectory, the processor may calculate the body tilt axis as the normalto the plane that passes through three distinct points of the handtrajectory. It may calculate the swing plane that is spanned by thevelocity vector of the sweet spot at impact and the bat longitudinalaxis at impact. It may calculate one or more swing quality metrics basedon any or all of the data described above, including for example basedon one or more of the time series of inertial sensor data, the time ofimpact, the trajectories of the hand position, sweet spot, and batlongitudinal axis, the body tilt axis, and the swing plane.

In one or more embodiments, the sweet spot position on the bat maycorrespond to any or all of an optimum location on the bat for strikingthe ball, a position on the bat that maximizes energy transfer or ballspeed, and a position on the bat that minimizes vibration when hittingthe ball.

In one or more embodiments, the longitudinal acceleration—theacceleration of the bat along its longitudinal axis—may be used tocalculate a rotational acceleration metric. The start of centripetalacceleration may be calculated as the time at or near a change in signof the longitudinal acceleration, and an early rotation time may becalculated as a fixed offset after this start of centripetalacceleration. The fixed offset may be for example in the range of 10 to50 milliseconds. A rotational acceleration metric may be calculated asthe difference between the longitudinal acceleration between the earlyrotation time and the start of centripetal acceleration.

One or more embodiments may calculate a rotation-on-plane ratio atpoints in time during the swing, and use this ratio to calculate anon-plane efficiency metric. This ratio may be based on angular velocityvalues transformed to a swing plane coordinate system with the z-axisalong the bat longitudinal axis, the y-axis normal to the swing plane,and the x-axis orthogonal to the y and z axes. The rotation-on-planeratio may be calculated as the ratio of the magnitude of the y-axisangular velocity to the magnitude of the vector sum of the x and y axisangular velocities. The on-plane efficiency may be calculated as theaverage of the rotation-on-plane ratio between the start of centripetalacceleration and the time of impact.

One or more embodiments may calculate a body-bat angle at points in timeduring the swing, and use this angle to calculate one or more connectionor disconnection metrics. The body-bat angle may be calculated as theangle between the bat longitudinal axis and the body tilt axis. Aconnection-at-impact metric may be calculated as the body-bat angle atthe time of impact. A connection-early metric may be calculated as thebody-bat angle at the start of centripetal acceleration. Adisconnection-at-impact metric may be calculated as the absolute valueof the difference between the connection-at-impact and 90 degrees. Adisconnection-early metric may be calculated as the absolute value ofthe difference between the connection-early and 90 degrees. Anaverage-disconnection metric may be calculated as the average of thedisconnection-at-impact and the disconnection-early.

One or more embodiments of the invention may include a swing analysissystem that calculates a rotational profile. A bat (or other equipment)may have an inertial sensor coupled to the bat; the sensor may includefor example an accelerometer, a gyroscope, and a network interface.Inertial sensor data may be captured at a sequence of times through aswing of the bat by a user. This data may be transmitted to a processorover a network connection, and the processor may analyze the data. Thisanalysis may include calculation of the bat trajectory through theswing, which may include the hand position and sweet spot positionthrough the swing. It may include calculation of the center of rotationof the swing, of a body lever between the center of rotation and thehand position, and of a bat lever from the hand position to the sweetspot position. A body rotation angle may be calculated as the anglebetween the body lever at any point in time and the initial body leverat the start of the swing. A hinge angle may be calculated as the anglebetween the bat lever and a tangent perpendicular to the body lever. Thebody rotation rate may be calculated as the rate of change of the bodyrotation angle, and the bat rotation rate may be calculated as the rateof change of the hinge angle. A rotational profile of the swing may thenbe calculated, which includes the body rotation rate over time, the batrotation rate over time, and the centripetal acceleration of the batalong the bat's longitudinal axis over time.

One or more embodiments may include a database with rotational profilesassociated with multiple users, and a swing analysis coupled to thedatabase that compares rotational profiles across users. The swinganalysis system may also generate a recommended bat for a user.

In one or more embodiments, the processor that analyzes sensor data maypartition the time sequence for the swing into phases. Phases may forexample include a load phase that starts at the start of swing, anaccelerate phase following the load phase that starts when thecentripetal acceleration changes from positive to negative, a peak phasefollowing the acceleration phase, and a transfer phase following thepeak phrase and extending to the end of swing when the bat impacts theball.

In one or more embodiments, the rotational profile may also include oneor more swing metrics. These metrics may be calculated for example fromany or all of the inertial sensor data, the body rotation rate, the batrotation rate, and the centripetal acceleration.

Swing metrics may include the peak loading acceleration, which is themaximum positive centripetal acceleration during the load phase. Theymay include the rate of acceleration, which is an average rate of changeof the centripetal acceleration during the accelerate phase. They mayinclude the peak acceleration, which is the minimum negative centripetalacceleration after the load phase and before the end of the swing. Theymay include the acceleration impulse, which is an integral of thecentripetal acceleration between the start of the accelerate phase andthe end of swing. They may include the time to peak force, which is thetime difference between the start of the accelerate phase and the timewhen the centripetal acceleration reaches its minimum negative valueafter the start of the accelerate phase.

Swing metrics may include the peak bat rotation rate, which is themaximum value of the bat rotation rate between the start of the loadphase and the end of the swing. They may include the peak body rotationrate, which is the maximum value of the body rotation rate between thestart of the load phase and the end of the swing. They may include aratio between the peak bat rotation rate and the peak body rotationrate.

One or more embodiments of the invention may enable an equipment fittingsystem that uses swing metrics to recommend equipment to a user. Theequipment may be for example, without limitation, a golf club or a bat.The system may include one or more inertial sensors, each with anaccelerometer, a gyroscope, and a network interface. Each sensor may becoupled to one or more pieces of equipment from a set of pieces ofequipment used by a user, for example as part of a testing or fittingsession. The sensors may capture data during swings by the user of eachpiece of equipment. This sensor data may be transmitted to a processorfor analysis. The processor may calculate swing metrics based on theinertial sensor data; metrics may include an acceleration metric, aspeed metric, and a momentum metric. A metrics score may be calculatedfor each piece of equipment from these metrics. For example, the metricsscore may be calculated as a weighted sum of the swing metrics. Thesystem may recommend an optimal piece of equipment for the user based onthe metrics score.

In one or more embodiments, a recommendation for an optimal piece ofequipment may also be based on factors such as a user feel scoreprovided by the user for each piece of equipment, an expert opinionscore provided by one or more experts for each piece of equipment, and aconsumer comparison score provided by consumers for each piece ofequipment. For example, the processor may calculate an overall score foreach piece of equipment as a weighted sum of the metrics score, the userfeel score, the expert opinion score, and the consumer comparison score.In one or more embodiments the weights for this weighted sum may bebased on user input.

Associated with each piece of equipment may be parameters such as alongitudinal axis, a sweet spot position, and an effective mass. Whenthe equipment is a bat, the effective mass may be for example 0.75 timesthe mass of the bat. The momentum metric may be equal to the effectivemass times the speed metric. The speed metric may be the speed of thesweet spot at an endpoint of the swing; the endpoint may be the time ofimpact with an object (such as a ball) or the time when the rotationalvelocity magnitude is at a maximum. The acceleration metric may be forexample a rate of change of the centripetal acceleration of the piece ofequipment along its longitudinal axis. For example, the processor maypartition the swing into phases such as a load phase, an acceleratephase, a peak phase, and a transfer phase, and the acceleration metricmay be the average rate of change of the centripetal acceleration duringthe accelerate phase.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the ideasconveyed through this disclosure will be more apparent from thefollowing more particular description thereof, presented in conjunctionwith the following drawings wherein:

FIG. 1 shows an overview flowchart of an embodiment that processessensor data in a swing plane reference frame to generate several swingmetrics for the swing of a baseball bat.

FIG. 2 shows a reference frame based on a swing plane defined by the batorientation and by the velocity vector of the bat at the time of impactwith the ball.

FIG. 3 illustrates transformation of a bat trajectory from a localsensor frame to the swing plane reference frame of FIG. 2 .

FIG. 4 illustrates various metrics derived from the swing planereference frame, including a total swing angle in the swing plane, anoff-plane swing angle, and a swing plane speed.

FIG. 5 illustrates derivation of a time to contact swing metric thatmeasures how quickly the batter responds.

FIG. 6 illustrates derivation of a swing tempo metric based on swingplane speed, which indicates how quickly the swing plane speed increasesthrough the swing.

FIG. 7 illustrates an embodiment that collects swing data from multipleusers into a swing database, and that analyzes this database to generatemethods of rating and classifying swings.

FIG. 8 illustrates an embodiment that analyzes swing tempo from multipleusers to determine a target zone for peak performance.

FIG. 9 shows an embodiment that provides feedback to a user on his orher swing by comparing the swing tempo to the target zone described inFIG. 8 .

FIG. 10 illustrates an embodiment that classifies swings into swingstyles based on a feature vector that combines multiple swing metrics;feedback to a user indicates the swing style as well as identifyingother players with similar swings.

FIG. 11 shows a potential issue that may arise when a sensor has alimited range and the actual motion of the bat exceeds this measurementrange during a time interval within the swing.

FIG. 12 illustrates an embodiment that addresses the limited rangesituation shown in FIG. 11 by extrapolating sensor data from before andafter the time interval, in this example using a cubic Bézier curve.

FIG. 13 illustrates an embodiment that extrapolates sensor data using aKalman filter to estimate values when the measurement range of thesensor is exceeded.

FIG. 14 illustrates an embodiment that tracks the trajectory of thesweet spot of a bat and that calculates swing metrics from this sweetspot trajectory.

FIG. 15 illustrates a reference frame used in one or more embodiments tomeasure bat motion and to calculate swing metrics; this reference framehas the origin at the sweet spot, a vertical z-axis, and the bat is inthe xz-plane at impact.

FIG. 16 shows another view of the reference frame of FIG. 15 , andillustrates several swing metrics including the bat forward velocity atimpact, the attack angle, and the swing plane tilt angle.

FIG. 17 shows a swing plane that is spanned by the bat's longitudinalaxis and the velocity of the sweet spot at impact.

FIG. 18 shows the off-plane distance between the bat sweet spot and theswing plane during the swing, and it illustrates swing metrics thatinclude the time when the bat is on-plane (within a specified thresholddistance from the swing plane), and the on-plane metric that measuresthe angular range of motion while the bat is on-plane prior to impact.

FIG. 19 illustrates an embodiment of a center of rotation calculation,which determines a point equidistant from the hand position on the batat multiple points on the swing.

FIG. 20 illustrates a two-lever model of a swing that is used tocalculate swing metrics such as a hinge angle between a bat lever and abody lever.

FIG. 21 shows a calculation of a commit event that may represent, forexample, when the wrist snaps to release the bat from a cockedorientation to complete a swing.

FIG. 22 shows an illustrative swing trajectory with several swing eventsannotated along the trajectory; it also illustrates a swing axis ofrotation and a body tilt metric derived from this axis of rotation.

FIG. 23 shows an embodiment that provides bio-feedback to the user forsetting posture or position or swing or any combination thereof viasound or AR/VR/MR visual displays, that enables working on postures,positions, swings and detecting proper or improper postures, positions,swings or portions thereof and to improve power and/or efficiency and toenable rehabilitation.

FIG. 24 shows an embodiment of the invention that calculates severalswing quality metrics from acceleration and angular velocity datacaptured by an inertial sensor on a bat; illustrative swing qualitymetrics include rotational acceleration, on-plane efficiency, andbody-bat connection.

FIG. 24A shows a variation of the embodiment of FIG. 24 that uses videocameras instead of inertial sensors to capture motion data.

FIG. 25 shows illustrative bat geometry data that may be used in one ormore embodiments to calculate swing quality metrics.

FIG. 26 shows illustrative processing steps that may be used in one ormore embodiments to calculate swing quality metrics; these steps mayinclude integrating acceleration and angular velocity data, detectingimpact, and calculating trajectories of bat orientation and of thepositions of the hands and the sweet spot on the bat.

FIG. 27 expands on the flowchart of FIG. 26 to show additional data thatmay be calculated to determine swing quality metrics, including a swingplane and a body tilt axis.

FIG. 28 illustrates determination of a final phase of a swing thatcorresponds to centripetal (negative) acceleration along a bat'slongitudinal axis.

FIG. 29 illustrates a method that may be used in one or more embodimentsto determine the start of the centripetal acceleration phase.

FIG. 30 illustrates a method of calculating a rotational accelerationswing quality metric as a change in acceleration a short time after thebeginning of the centripetal acceleration phase.

FIG. 31 shows illustrative rotational acceleration for three types ofswings.

FIG. 32 shows a coordinate system defined using the swing plane, andangular velocities along the coordinate axes of this coordinate system.

FIGS. 33A and 33B show illustrative calculations of an on-planeefficiency swing quality metric for two types of swings, one with a highvalue of on-plane efficiency and the other with a relative low value ofon-plane efficiency.

FIG. 34 shows an illustrative definition of a body-bat connection metricusing the bat direction and the body tilt axis.

FIGS. 35A and 35B show illustrative calculations of a disconnectionmetric, which is the offset between the connection metric and 90degrees.

FIG. 36 shows illustrative body-bat connection values at the start ofcentripetal acceleration and at impact.

FIG. 37 shows illustrative values for three swing qualitymetrics—rotational acceleration, on-plane efficiency, and body-batconnection—for three players.

FIG. 38 shows an illustrative swing analysis system that calculates arotational profile from data obtained from an inertial sensor on thebat.

FIG. 39A illustrates use of rotational profile data or other swinganalysis data to recommend equipment or to fit equipment for a user.

FIG. 39B shows an illustrative equipment fitting process that comparesswing metrics obtained from swings using different equipment options.

FIG. 40 shows illustrative components of a rotational profile:centripetal acceleration, body rotation rate, and bat rotation rate.

FIG. 41A shows illustrative centripetal acceleration curves for baseballplayers of different skill levels.

FIG. 41B shows illustrative body rotation rate and bat rotation ratecurves for baseball players of different skill levels.

FIG. 42 illustrates partitioning a swing into four phases: load,accelerate, peak, and transfer.

FIG. 43 shows five illustrative metrics that may be calculated from thecentripetal acceleration curve.

FIG. 44 shows three illustrative metrics that may be calculated from thebody rotation rate and bat rotation rate curves.

FIG. 45 shows an example of calculating a rotational profile for a golfswing.

FIG. 46 shows an equipment fitting system that calculates a metricsscore for each piece of equipment from data on acceleration, speed, andmomentum.

FIG. 47 shows illustrative inputs and calculations to generate a metricsscore for equipment fitting.

FIG. 48 shows acceleration and speed metrics for swings by two playersusing three different bats to illustrate identification of a bat foreach player that optimizes the player's hitting power.

FIG. 49 shows a different set of metrics—on plane efficiency and attackangle—that may be used to compare bats based on how effectively a playercontacts a ball.

FIG. 50 shows an illustrative fitting system that combines a metricsscore with other inputs to compare equipment.

FIG. 51A illustrates identification of the endpoint of a swing bydetecting an impact event;

FIG. 51B shows definition of a swing endpoint when there is no impact,using the moment of peak angular velocity.

DETAILED DESCRIPTION OF THE INVENTION

An equipment fitting system that compares swing metrics will now bedescribed. In the following exemplary description numerous specificdetails are set forth in order to provide a more thorough understandingof the ideas described throughout this specification. It will beapparent, however, to an artisan of ordinary skill that embodiments ofideas described herein may be practiced without incorporating allaspects of the specific details described herein. In other instances,specific aspects well known to those of ordinary skill in the art havenot been described in detail so as not to obscure the disclosure.Readers should note that although examples of the innovative conceptsare set forth throughout this disclosure, the claims, and the full scopeof any equivalents, are what define the invention.

FIG. 1 shows an overview of an embodiment of the invention. User 101swings a baseball bat 102 to hit an incoming ball 103. Data is collectedthroughout the swing from sensor 104 attached to the bat. Sensor 104 mayincorporate any type of sensor technology or technologies to measure anyquantities, such as for example any aspects of the motion, position, ororientation of the bat. The sensor may be coupled with the proximal endof the bat, the distal end of the bat or anywhere in between. In one ormore embodiments the sensor 104 may comprise two or more sensors atdifferent locations on the bat. For example, without limitation, sensor104 may contain any or all of a three axis accelerometer 105, a threeaxis gyroscope 106, and a three axis magnetometer 107. These sensortypes are illustrative; one or more embodiments may use sensor data fromany type or types of sensors to track the swing of bat 102. In one ormore embodiments the sensor 104 may not be physically attached to thebat; for example, the sensor may be stationary and it may observe themoving bat using technologies such as video, radar, LIDAR, orultrasound. In one or more embodiments, data from multiple types ofsensors may be combined using sensor fusion. For example, sensor datafrom an inertial sensor on a bat may be fused with radar data or otherinformation from external devices to calculate a bat trajectory. Sensorsmay measure motion or other parameters on any number of axes. Sensorsmay measure these parameters at any desired frequency; highermeasurement frequency may for example support more detailed analysis ofthe swing. For example, without limitation, sensor 104 may collect dataonce per second, ten times per second, one hundred times per second, onethousand times per second, ten thousand times per second, or atfrequencies above ten thousand times per second.

In the embodiment shown in FIG. 1 , bat 102 is a baseball bat. One ormore embodiments may obtain and analyze data for the swing of any typeof bat or similar object, including for example, without limitation, abaseball bat, a softball bat, a cricket bat, and in one or moreembodiments, a tennis racket, a table tennis racket, a badminton racket,a squash racket, a racquetball racket, a golf club, a polo mallet, ahockey stick, a field hockey stick, and a lacrosse stick or any othertype of equipment that involves a swing.

Data from sensor 104 is obtained in step 110. One or more embodimentsmay use any data transfer technology or technologies to obtain sensordata. For example, without limitation, data may be transferred over awireless network, over a wired network, or using a data storage mediumthat is moved from one system to another. Data may be obtained in realtime during a swing, obtained after a swing occurs, or obtained using acombination of real-time transfer and transfer after a swing event.

Steps 120 through 170 analyze data from sensor 104 to characterize theswing, resulting in swing metrics 180. These steps may be performed inany order, or in parallel. These steps may be performed on any system orcombination of systems. For example, without limitation, any or all ofthese steps may be performed on a computer, a mobile computer, a laptopcomputer, a notebook computer a desktop computer, a tablet computer, amobile phone, a smart phone, a smart watch, a microprocessor, a server,or a network of any of these devices. In one or more embodiments thesensor 104 may contain a processor or processors that perform some orall of the steps 110 through 170.

Step 120 determines the time of impact between bat 102 and ball 103.This step may for example detect a signature in the sensor data thatindicates a collision. For example, if sensor 104 includes anaccelerometer such as accelerometer 105, a rapid spike in accelerationmay be a signature of an impact. Similarly, if sensor 104 includes agyroscope such as gyroscope 106, a rapid reduction in angular velocitymay be a signature of an impact. One or more embodiments may for exampleuse sensors that directly measure impact, such as pressure sensors orcontact switches. In one or more embodiments, a swing endpoint may bedefined even if the bat does not hit the ball, for example duringpractice swings, air swings, or strikes. This swing endpoint may bebased for example, without limitation, on parameters such as thelocation of the bat relative to the plate or to an incoming ball, theaim angle of the bat, or the point in time when the bat achieves maximumvelocity or maximum angular velocity. A calculated swing endpoint may beused instead of an actual impact time for any of the subsequent metriccalculations described below.

Step 130 calculates a trajectory of the bat 102 from a starting point ofthe swing through the impact time determined in step 120. In one or moreembodiments the trajectory may also extend beyond the impact or prior tothe start of the swing. The bat trajectory may be a time series ofmotion data samples, each of which represents the state of the bat at apoint in time during the swing. For example, each sample may includedata on any or all of the bat's position, orientation, velocity, angularvelocity, acceleration, or angular acceleration. In one or moreembodiments a sample may include data for multiple locations on the bat.Methods to calculate an object's trajectory from motion sensor data areknown in the art. For example, one or more embodiments may use inertialnavigation algorithms known in the art to calculate the position andorientation of the bat over time from acceleration data (for examplefrom accelerometer 105) and from angular velocity data (for example fromgyroscope 106). Data from other sensors, such as for examplemagnetometer 107, may for example provide redundant measurements tocorrect errors in inertial navigation algorithms.

Because the orientation and position of sensor 104 changes throughoutthe swing, the bat trajectory calculated in step 130 may not be in aconvenient form for analysis. Therefore, in step 150 a standardizedreference frame is defined based on the swing itself. We refer to thisreference frame as the swing plane reference frame. In step 160 the battrajectory is transformed to this reference frame. In step 170 thetransformed trajectory is used to analyze the swing, and to generate oneor more swing metrics describing and characterizing the swing.Illustrative swing metrics 180 describe for example the timing of theswing, the speed of the swing, and the angles traversed during theswing.

FIG. 2 illustrates definition and calculating of the swing planereference frame. This reference frame is defined by the bat'sorientation and motion at the time of impact between the bat 102 and theball 103. A swing plane 212 is defined by two axes: a first axis 210 isthe longitudinal axis of the bat (along the bat's long dimension); asecond axis 211 is in the direction of the bat's velocity at the time ofimpact. The velocity vector at impact may also be calculated as atangent vector to the bat's instantaneous rotation round the angularvelocity axis. This impact velocity vector 211 may be calculated orobtained from the bat trajectory. In one or more embodiments a specificpoint on the bat, such as for example the sweet spot, may be used todefine the impact velocity vector. The swing plane 212 is the planespanned by the vectors 210 and 211. To complete the reference frame, athird orthogonal off-plane axis 213 is selected as the normal vector tothe plane 212. The swing plane 212 defined by the axes 210 and 211provides a reference frame that can be calculated from data generated bybat sensor 104. Other planes of rotation that may be relevant to thekinematics of the swing include for example the rotational plane 221 forthe batter's shoulders, and the rotational plane 222 for the batter'ships. In one or more embodiments additional sensors, for example sensorsattached to the batter's shoulders and hips, may be used to calculatethese body rotational planes in addition to the swing plane 212.

In the example shown in FIG. 2 , sensor 104 has a local reference framein which sensor data is measured. This local reference frame in generalmay have a completely different orientation from the swing planereference frame defined by axes 210, 211, and 213. For example, thesensor local reference frame may have axes 201, 202, and 210; in thisexample one axis of the sensor local reference frame is aligned with thebat longitudinal axis, but the other axes are in arbitrary directionsdue to the rotational symmetry of the bat around this axis. Tofacilitate standardized analysis of swings and comparison of swingsacross players, bat trajectory information is transformed from thesensor local reference frame into the swing plane reference frame. FIG.3 illustrates this transformation. Bat trajectory 301 includes motiondata samples at various points in time, such as for example points 302,303, and 304. These samples may include any information on the state ofthe bat, such as position, orientation, or derivatives of these valueslike velocity and angular velocity. For illustration, the bat trajectory301 is shown as a single curve in three dimensional space (for exampleas a curve of bat position over time); however, in one or moreembodiments the bat trajectory may include any data with any number ofdimensions. In the sensor local reference frame defined, forillustration, by axes 201, 202, and 210, each sample point hascoordinates such as coordinates 305 for point 304. Transformation 310maps the sample points into the swing plane reference frame, for exampleusing a rotation of the axes 201, 202, and 210 into axes 210, 211, and213. For example, in the swing plane reference frame, point 304 on thebat trajectory 301 has coordinates 306.

One or more embodiments of the invention may analyze the bat trajectoryin the swing plane reference frame to measure and characterize theswing. FIG. 4 shows illustrative metrics for angular change that aredefined relative to the swing plane reference frame. Bat trajectory 401is a three dimensional curve in the three dimensional swing planereference frame 410 defined by axes 210, 211, and 213. Trajectory 401has starting point 420, representing a start of the swing, and endpoint421, representing for example the time of impact between the bat and theball. This curve may be projected onto the two-dimensional swing plane212 defined by axes 210 and 211, and various metrics may be calculatedfrom this projection. For example, the 2D curve 402 is the projection ofthe bat trajectory 401 onto plane 212. As the curve 402 proceeds fromthe starting point to the endpoint of the trajectory, it subtends anangle 403 (Δθ_(sp)) in the swing plane (with vertex at the origin). Thisangle 403, which we refer to as the total swing angle, is a swing metricthat indicates the total amount of bat movement during the swing in theswing plane. Similarly, the bat trajectory 401 may be projected onto aplane 412 orthogonal to the swing plane, and the angle 407 subtended bythe projected trajectory is a different swing metric that we refer to asthe off-plane angle. The total swing angle metric and the off-planeangle metric provide a useful characterization of how the batter ismoving the bat through the swing. Projection of the trajectory 401 ontoswing plane 212 also provides a measure of the instantaneous angularvelocity 406 of the trajectory at any point in time, such as atillustrative point 404. This instantaneous angular velocity in the swingplane, which we refer to as the swing plane speed, is a more usefulmetric of the bat's motion than for example the total linear velocity ofthe bat, which includes an off-plane component of velocity that is notas relevant for the power of the swing. The swing plane speed 406 may becalculated for example as the derivative of the instantaneous angle 405between the point 404 on the projected trajectory 402 and the axis 210.In one or more embodiments that include a gyroscope, which measuresangular velocity directly, the swing plane speed may be calculated byprojecting the measured angular velocity onto the axis orthogonal to theswing plane 212.

The curve of swing plane speed over time through the swing providesadditional useful information about the swing. FIG. 5 shows anillustrative curve 501 of the swing plane speed 406 as a function oftime. The curve typically increases through the swing as the batteraccelerates the bat. The swing plane speed reaches a maximum value 505during the swing. For some swings, the peak speed 505 may occur at thetime of impact 502; however, this is not necessarily the case for allswings. The impact swing plane speed 506 is an important swing metricsince it greatly affects the distance and power of the hit. The swingplane speed curve may be used to define an unambiguous point in time forthe start of the downswing of a swing: this start of downswing 503 maybe defined as the last point in time when the swing plane speed is zeroprior to the impact. This definition is based on an unambiguous physicalevent rather than an arbitrarily defined threshold crossing. Thisprovides a clear advantage in terms of metric consistency and physicalsignificance. If there is no zero crossing, as is the case in certainswing styles, we define the start of downswing where the slope andmagnitude of the swing plane component meet certain threshold criteria.This fallback definition does not provide the clear advantages of thezero crossing; however, because it is based on the swing planecomponent, it provides greater consistency than a definition based onvector magnitude, particularly across heterogeneous swing styles wheremuch of the variability (e.g., bat waggle) occurs in the off-planecomponent.

Using the start of downswing 503 and the time of impact 502, a totalswing time, which we refer to as the time to contact metric, may bedefined as the difference 504 between the impact time 502 and the startof downswing time 503. This time to contact metric is an importantmetric related to the batter's ability to read the pitch.

The rate at which the swing plane speed increases through the swing alsoprovides a useful metric. FIG. 6 illustrates a method to standardizethis metric by measuring the fraction of the peak speed achieved at thehalfway point of the swing. To allow meaningful comparison acrossplayers with different swing styles, the swing plane speed curve isnormalized so that swing plane speed is measured as a percentage 605 ofthe peak speed. Thus the normalized swing speed curve starts at zero atthe start of downswing, and increases to 100% at the peak speed. Ahalfway point 602 is defined for the swing, and the fraction 603 of thepeak speed at this point is defined as the swing tempo metric 604. Inone or more embodiments the halfway point may be defined as halfwaybetween the start of downswing and the time of impact. However,empirical analysis of swings shows that a more robust halfway point maybe defined by selecting a swing onset time 601 as a time at which theswing plane speed reaches a specified small fraction of the peak speed,such as for example 10%, and by defining the halfway point as halfwaybetween the swing onset time and the time of impact.

This definition of the swing tempo metric is based on the insight fromcomparing statistical distributions, where the greatest variability indeviation from an ideal curve occurs at the half-way point between twofixed endpoints. The significance of this metric comes from anunderstanding of the kinematic chain (hips, shoulders, arms, wrists) fortransferring energy from the body to a baseball bat. A rotationallyefficient swing will derive a certain amount of energy from the hips andshoulders compared to the arms and wrists. We can infer how rotationallyefficient a baseball swing is by the percentage of speed in the “body”half of the swing relative to the “arm” half. An ideal swing tempo rangeis learned from empirical data collected from elite-level batters.Deviation from the ideal tempo range, either high or low, is used toprovide feedback and prescribe drills to the batter in order to improveperformance. A low tempo typically indicates that the swing is dominatedby arms (e.g., casting), while a high tempo indicates that a swing isdominated by body (at the expense of bat control).

In one or more embodiments, additional tempo metrics may be defined atother points in a swing, in addition to the halfway point tempo metricdescribed above. For example, without limitation, an early tempo metricmay be defined as the fraction of peak speed achieved at the 25% pointof the swing, a mid-tempo metric may be defined as the fraction of peakspeed achieved at the 50% point of the swing (as discussed above), and alate tempo metric may be defined as the fraction of peak speed achievedat the 75% point of the swing. The three tempo metrics may isolate theeffect of different segments of the kinematic chain of the swing; forexample, the early tempo metric may characterize the rotation of hipsand torso, the mid-tempo metric may characterize the rotation of thetorso and arms, and the late tempo metric may characterize the rotationof the arms and bat. These percentages are illustrative; one or moreembodiments may measure swing tempo at any point or points in a swing.

In one or more embodiments, swing data and swing metrics may becollected from multiple users and organized in a swing database forfurther analysis. FIG. 7 illustrates an embodiment that collects datainto swing database 701 from multiple types of users, including forexample, without limitation, experts 702, professionals 703, amateurs704, novices 705, and instructors 706. Data in the swing database mayinclude for example, without limitation, sensor data 710, battrajectories in the swing plane frame 711, and swing metrics 712 (suchas for example the total swing angle, off-plane angle, time to contact,impact swing plane speed, and tempo metrics described above). Multiplemetrics may be combined into feature vectors 713 that may be used toclassify, categorize, compare, or analyze swings. Data from the databasemay be used for various analysis procedures 720, which may include forexample any or all of modeling swings and batters, data mining thedatabase for patterns or trends, and applying machine learningtechniques to learn relationships, functions, or categories. Outputs ofthe analyses 720 may include for example identification of bestperformances 721 that flag certain swings or groups of swings asillustrative of ideal or maximum performance; factors affectingperformance 722 that identify swing characteristics that contribute toor detract from high performance; performance rating functions 723 thatrate swings on how close they are to ideal performance levels;classifications of swing styles 724 that map swings into categoriesreflecting similar characteristics or similar performance; and matchingof swings to similar players 725 that indicate which other swings orother players are most similar to a given swing or player.

FIG. 8 illustrates an example of the data analysis methods describedwith respect to FIG. 7 , using the swing tempo metric defined above.Using swing database 701 as input, data analysis and data mining process720 compares swing plane speed curves across players to determinefactors affecting performance 722. This analysis indicates that bestperformance occurs when swing tempo is in a target zone 802, for examplein a range between 804 and 803. This analysis uses normalized swingplane speed curves for the swings in database 701, with the swing planespeed axis normalized to the percentage of peak speed 605, and the timeaxis 801 normalized to a percentage of swing time between swing onset(0%) and impact 502 a (100%). The normalized swing plane speed athalfway point 602 a (50%) is the swing tempo metric for each swing.

Using the analysis illustrated in FIG. 8 , an individual swing may beevaluated by comparing it to the empirically derived criteria for bestperformance. FIG. 9 illustrates an example with batter 101 generating aswing plane speed curve 901 for a swing. The measured swing tempo 902for this swing is compared to the target zone 802 in order to rate theswing's performance. Feedback is then provided to batter 101, forexample on computer screen 903. This feedback provides the swing tempometric 902, as well as a performance rating 904 that is based oncomparing the swing to performance criteria derived from empiricalanalysis. The feedback may also include specific critiques such as 905that diagnose the swing or suggest corrections or improvements.

One or more embodiments may provide feedback to a batter or to otherusers (such as a coach or trainer) using any desired method or system.For example, without limitation, feedback may be displayed on anycomputer, laptop, notebook, tablet, mobile phone, smart watch, orwearable device. Feedback may be provided using a specific app, ortransmitted via general messaging systems such as email or textmessages. Feedback may be audio, visual, haptic, or any combinationthereof.

FIG. 10 continues the example of FIG. 9 to illustrate additionalanalysis and feedback for a swing based on comparisons with swings in aswing database. In this example, a feature vector 1001 is generated fora particular swing by batter 101. For illustration, this feature vectoris a combination of the swing tempo and the impact swing plane speed.One or more embodiments may generate feature vectors using anycombinations of metrics or of any data derived from sensor data or battrajectories. Swings from swing database 701 are compared on grid 1002using this feature vector, and are analyzed (for example using clusteranalysis techniques known in the art) to categorize swings into a set ofswing styles. For example, the analysis may partition swings into threeswing styles 1004, 1005, and 1006. The feature vector 1001 correspondingto the swing by batter 101 places the swing into swing style cluster1006. Feedback to the batter indicates this swing style 1020. Inaddition, the batter's swing may be matched against typical swings fromother users to provide feedback 1021 that identifies other users withswings that resemble the batter's swing.

In some situations, one or more of the sensors that measure the motionthe bat may have insufficient range to measure the complete motionthroughout the entire swing. FIG. 11 shows an example of this situationwhere the sensor 104 on bat 102 includes accelerometer 105 with range1101, and gyroscope 106 with range 106. Taking the angular velocityaround the x-axis of the sensor as an illustrative example, the actualx-axis angular velocity 1103 exceeds the upper limit 1104 of measurementrange 1102 during time interval 1105. Therefore, the measured sensorvalues 1106 cannot track the true values 1103 of the motion during thisinterval 1105. Instead the measured value 1107 during this interval issaturated at the upper limit 1104. This saturation may affect theaccuracy of swing metrics. This example using the x-axis of thegyroscope is illustrative; a similar issue may occur with any sensor(including for example the accelerometer 105 as well as the gyroscope106) and with data from any axis of any sensor.

To address this issue, one or more embodiments of the invention mayextrapolate sensor data from prior to or after the time interval 1105when the sensor is saturated. Extrapolation may also be used when sensordata is unavailable for a period of time for any other reason, forexample because of a limited sampling rate, a recalibration period, or adefective sensor. Extrapolation may be used for any sensor or sensors,or any axis of any sensor or sensors. Embodiments may use any method toextrapolate sensor data into any time interval. FIG. 12 illustrates anembodiment that extrapolates sensor data from both endpoints of the timeinterval by constructing a Bezier curve 1200 for the values in theinterval. In this example, the curve 1200 is a cubic Bezier curvedefined by the four control points 1201, 1202, 1203, and 1204. This isillustrative; one or more embodiments may use Bezier curves or any othersplines or curves of any order. Control points 1201 and 1204 match thevalues of the sensor measurements 1104 at the endpoints of interval1105. The internal control points 1202 and 1203 are chosen to match theslopes of curve 1104 at these endpoints. Specifically, the tangent value1205 of the curve 1104 at point 1201 is the slope of the line betweencontrol points 1201 and 1202, and the tangent value 1206 of the curve1104 at point 1204 is the slope of the line between control points 1203and 1204. Points 1202 and 1203 may also be chosen to limit for examplethe maximum value of the curve 1200 in the interval.

One or more embodiments may select control points for a Bezier curve insuch a way as to satisfy the initial and/or final conditions (magnitudeand slope) and also to satisfy additional constraints on the maximumabsolute value and maximum extrapolation duration. For two-sidedextrapolation (no impact events), four control points may be used asshown for example in FIG. 12 : the initial and final points are placedwhere the curve crosses the saturation threshold, and two interiorcontrol points are along a line matching the slope of the curve at somedistance, which is constrained by some maximum time duration and by amaximum absolute value. This approach provides control of the shape ofthe extrapolation curve better than a cubic polynomial fit, which willmatch the same slope and value constraints but may exceed the otherphysical constraints. If the initial or final edge of the saturationinterval is an impact event, then the unconstrained edge may berepresented by a single control point, resulting in a three-point Beziercurve. Again, the time and value for this single control point may beselected to achieve the desired shape of the extrapolated curve into theimpact event. Because a Bezier curve is not parametric in time, it maybe necessary to resample the extrapolated curve at the original sampletimes. This type of Bezier extrapolation may be applied to an individualsaturated sensor axis (independent of the other components) or acomposite value (e.g., the x-y resultant or total vector magnitude). Theshape of the composite curve may be easier to model or constrain thanthe underlying individual components for particular kinematic events,resulting in increased accuracy of the extrapolated result. If theunderlying component values are needed, they can be obtained by solvingfor the unknown saturated component(s) from the extrapolated compositeresult and unsaturated component values (the result will beunder-determined if more than one component is saturated).

Another approach to extrapolation that may be used in one or moreembodiments is to use a Kalman filter (or a variation of a Kalman filterlike an Extended Kalman Filter or an Unscented Kalman Filter). FIG. 13illustrates an example that uses this approach. Kalman filter 1301incorporates a kinematic model 1302 of the bat 102. The system state1303 is estimated for each sample point, and this estimate is correctedbased on measurements 1304. The state 1303 for example may include theposition r(t) and the orientation Q(t) of the bat, and the measurements1304 may include for example accelerometer values a_(x), a_(y), a_(z)and gyroscope values ω_(x), ω_(y), ω_(z). During time intervals when oneor more measurements are not available or are saturated, such as x-axisangular velocity 1306 during time interval 1105, the filter 1301continues to predict state values 1303. Therefore, the curve 1104 can beextrapolated to curve 1308 through interval 1105; for example, theorientation 1307 may be differentiated to estimate the x-axis angularvelocity 1308 in this interval.

In general, one or more embodiments may use a recursive state spaceestimator (e.g., Kalman filter) with a kinematic model of the physicalbody or equipment being measured. The state-space propagation model maybe used to impose appropriate physical constraints. The state spaceestimate and its uncertainty (covariance) may be updated using thenon-saturated measurements from the various sensors. An estimate of themissing (saturated) parameter may then be derived from the state spaceestimate. Likewise, the uncertainty in the estimated parameter may bederived from the model uncertainty. Either the state space propagationmodel or the measurement model (or both) may be non-linear, in whichcase a linearized (EKF) or sigma-point (UKF) filter may be used.Finally, the uncertainty in the extrapolated time series (or the statespace estimate itself) may be propagated to derived metrics. Forexample, in a baseball swing like the swing illustrated in FIG. 13 , thegyroscope may be saturated into impact, which affects the accuracy ofthe swing speed measurement. Using this approach, it is possible toestimate the actual swing speed and provide an uncertainty interval(error bars).

In one or more embodiments, a swing of a bat or similar equipment may bedecomposed into key events and metrics that provide insight into overallswing quality. Some of these events and metrics may be related to orderived from the trajectory of a sweet spot of the bat. FIG. 14 shows anillustrative swing of bat 102 by batter 101. The bat is equipped with asensor 104, which may for example include a motion sensor with anaccelerometer and a gyroscope. One or more embodiments may obtain sensordata from sensor or sensors 104, and may use this sensor data tocalculate the trajectory 1402 over time of sweet spot 1401 of the batthrough all or a portion of the swing. The sweet spot location on a batmay be determined by any desired method. For example, several commondefinitions for the sweet spot of the bat are that it produces themaximum energy transfer to the ball, that it produces the maximum battedball speed, or that it results in the least vibrational sensation(sting) in the player's hands. These results are not always produced bythe same spot on a bat. In addition, the spot may vary based on bat type(wood or aluminum), weight, shape, and other factors. For a morein-depth discussion of the definition, size, and location of the sweetspot for different bat types, see for example Daniel A. Russel, “Physicsand Acoustics of Baseball and Softball Bats.”

In one or more embodiments, an illustrative definition of a sweet spotmay be a location somewhere between four and eight inches from the tipof the bat, such as for example a single point on the centerline of thebat six inches from the tip.

In one or more embodiments, data from sensor 104 may be integrated orotherwise analyzed to estimate the sensor velocity and position in aninertial (world) coordinate frame. The known position of the sweet spotrelative to the sensor may then be used to calculate the sweet spottrajectory 1402 in this reference frame. In one or more embodiments, theworld reference frame may be defined as illustrated in FIG. 15 , whichshows the bat at the point of impact with a ball (or at another point intime defined as a real or virtual time of impact). The origin of thereference frame is at the sweet spot of the bat 1401 at the moment ofimpact. Gravity is in the −z direction; hence the z axis 1513 pointsvertically upward. The world coordinate system is not based on anabsolute horizontal reference point such as home plate or absolutenorth. Instead, the world frame is rotated so that the bat longitudinalaxis 1501 is in the xz plane pointing in the +x direction 1511 (forright handed batters) or −x direction (for left-handed batters). Theforward velocity of the bat is in the yz plane pointing in the +ydirection 1512. Because of this definition, the actual orientation ofthe world coordinate frame will vary from swing to swing.

FIG. 16 shows a close-up view of the reference frame illustrated in FIG.15 , shown again at the point of impact of the swing. The referenceframe origin is the location 1401 of the sweet spot of the bat atimpact. The −z axis 1513 a is in the direction of gravity, pointingvertically downward. Bat longitudinal axis 1501 is in the plane definedby the x axis 1511 and the −z axis 1513 a. The y-axis 1512 isperpendicular to the x-axis and to the z-axis. In general, the bat maynot be horizontally level at the time of impact; instead there may be anonzero angle 1603 between the bat axis 1501 and the (horizontal) x-axis1511, which is referred to as the vertical bat angle. Vertical bat angleis defined as the vertical direction of the bat with respect tohorizontal at impact. Vertical bat angle is negative below horizontaland positive above horizontal. The swing plane tilt angle 1603 is thevertical bat angle at the moment of impact. The swing plane tilt angleis usually negative, meaning the bat is pointing toward the ground. Alevel bat would result in a swing plane tilt angle of 0°. Swing planetilt angle is important for understanding adjustability and correlationsto pitch types and locations. Pitch location will determine changes inthe bat angle at impact. Adjusting the swing plane tilt angle to meetthe pitch should be done early in the swing in order to achieve maximumefficiency. Adjustment later in the swing drains energy from the speedof the bat. The swing plane tilt angle should match the location of thepitch. Steeper angles are required for low, inside pitches, andshallower angles are required for high, outside pitches.

The velocity of the bat at impact may also in general not be horizontal;the attack angle 1602 is the angle of the bat's forward velocity atimpact 1601 with respect to the horizontal y-axis 1512. Attack angle isnegative below horizontal and positive above horizontal. A positivevalue indicates swinging up, and a negative value indicates swingingdown, where zero is perfectly level. Attack angle is important for tworeasons: First, matching the bat path to the pitch path increases thelikelihood of contact. Because the pitch is thrown from an elevatedmound, it is typically on a downward angle as it crosses the plate.Therefore, a positive attack angle provides more opportunity to executeagainst a variety of pitches, which vary in height, speed, and angle.Second, a positive attack angle will usually maximize launch distance,increasing the scoring value of the at-bat. The average fastball crossesthe plate at a 6° downward angle, while an average breaking ball crossesthe plate at 10°. Other factors include swing speed and style, pitchvelocity and location, and game situation. Given the variation inincoming pitch descent angles and desired launch angle, the optimalattack angle is usually between +2° to +14° degrees. In a real gamescenario, adaptation may be required to put the ball in play. The idealattack angle results in the maximum distance for a given bat speed. Forslow bat speeds, the ideal attack angle is around 21°, and it getssmaller with increasing speed. Discussions of ideal launch angle, exitspeed, and scoring value appear for example in Nathan, “Optimizing theSwing,” at www.hardballtimes.com/optimizing-the-swing, and in Arthur,“The New Science of Hitting,” atwww.fivethirtyeight.com/features/the-new-science-of-hitting.

The bat forward velocity 1601 is the projection of the velocity vectorof the sweet spot onto the plane perpendicular to the bat longitudinalaxis 1501; it ignores any speed in the direction of the bat axis 1501.

FIG. 17 illustrates a definition of a swing plane from which variousswing metrics may be derived. Swing plane 1701 may for example bedefined as a plane through the sweet spot 1401 which is spanned by thebat longitudinal axis 1501 at impact and by the bat forward velocity1601 at impact. This swing plane is oriented so that it contains boththe length of the bat and bat velocity at the moment of impact. Theswing plane normal vector may found by normalizing the cross product ofthe bat length and bat velocity vectors. The normal vector is centeredat the sweet spot of the bat at the moment of impact, i.e., at (0, 0,0).

A swing may be analyzed for example by decomposing the motion into swingplane versus off-plane components. Off-plane motion may for example becharacterized by the distance of the sweet spot of the bat from theswing plane at any moment in time. FIG. 18 illustrates this distance ofthe sweet spot 1401 to the swing plane 1701 at several points in a swingprior to impact. For example, at the position of the bat shown in thefigure, the off-plane distance is 1801. As the swing progresses towardsimpact, the sweet spot approaches more closely to the swing plane 1701.When the distance reaches a specified threshold 1802, the swing isconsidered “on-plane” at that moment (provided that it remains at orbelow this distance from that moment until impact). For example, thethreshold may be set to 3 inches.

Based on the distance between the sweet spot and the swing plane, anon-plane metric may be defined as the total angular range of motion (forexample in degrees) of the swing where the sweet spot of the bat iswithin the threshold value (such as three inches) from the swing plane.For example in FIG. 18 the on-plane metric is the angle 1805 between theray 1803 at the on-plane event and the ray 1804 at the impact event.This metric measures an aspect of the quality of the swing because theplayer typically wants the energy from the body and arms to increaseforward bat speed rather than change its direction. Changing batdirection takes more energy as bat speed increases, so an efficientswing gets on plane early and stays on plane as it approaches impact.Ideally, a batter will read the pitch early and adjust the entire bodyto align the swing plane with the pitch location. This enables maximumbat speed for every pitch type. In one or more embodiments, the systemmay report the percentage of total velocity that is generated while thebat in on plane. For example, if the velocity is 40% of the peak whenthe bat gets on plane, then the “on plane” metric is 60%.

One or more embodiments may analyze the motion of a position on the batwhere the hands grip the bat, in addition to or instead of analyzing themotion of the bat sweet spot. FIG. 19 illustrates an embodiment thatdetermines a center of rotation 1903 for a swing by determining theposition of the hands at three points in the swing, at location 1902 a,1902 b, and 1902 c. The center of rotation is selected for example asthe point 1903 that is equidistant from these three points. One or moreembodiments may use any point or points on hands trajectory 1901 todetermine one or more centers of rotation for the swing. For example,point 1902 a may be selected as the time when the xy magnitude of thegyroscope value from the sensor is at 50% of its impact value; point1902 b may be selected as the time when the xy magnitude of thegyroscope value is at 80% of its impact value; and point 1902 c may beselected as the impact time. Using the hand positions at these times,the center of rotation may be calculated using the formula for thecircumcenter of a triangle defined for example inen.wikipedia.org/wiki/Circumscribed circle.

Three points on hands trajectory 1901 also define a plane, and thereforedefine an axis of rotation through the center of rotation 1903 that isperpendicular to that plane. The orientation of this axis of rotationmay also be used in one or more embodiments as a metric describing theswing. The three points that define the center of rotation lie in aplane that is typically tilted downward in front of the body. The axisof rotation may be calculated for example using the cross product of anytwo of the radius vectors from the center of rotation calculation.

In one or more embodiments, a two-lever model may be used to describeand analyze a swing. During the early part of the downswing, anexperienced batter rotates the core, arms, and bat as a single,connected unit. Then the batter commits by snapping the wrist, whichmoves the tip of the bat away from the body. The elbow may also extend,depending on ball location. This optimal kinematic sequence results inmaximum speed and control.

The kinematic chain includes core, shoulder, elbow, and wrist rotation.In some situations, it may not be feasible to measure all thesemovements directly using, for example, a single inertial sensor on thebat. Instead, one or more embodiments may use a simplified two-levermechanical model to distinguish “body” rotation from “bat” rotation. Thebody contribution ends at the hands. It measures rotation around thebody center of rotation, which is primarily core, shoulder, and someelbow extension. The bat component measures motion around the handposition, which is primarily due to elbow and wrist rotation. In aconnected swing, the shoulder and elbow contributions are small, and thebody component of our model closely approximates core body rotation.

FIG. 20 illustrates a swing model that employs a simple two-levermechanical system. This model focuses on the swing-plane and ignores anyoff-plane motion, which is characterized independently. The body leveris hinged at the body center of rotation and ends at the hand position.The bat lever is hinged at the hand position and extends along the axisof the bat. This model is illustrated in FIG. 20 . Body lever 2001extends from center of rotation 1903 to hand position 1902, and batlever 2002 extends from hand position 1902 to sweet spot 1401.

Total bat speed is a combination of body rotation and bat rotation. Thebody ratio may be calculated the percentage of total rotation that isattributed to the body. An efficient swing uses both the body, arms, andwrists in the appropriate kinematic sequence. A swing that is mainlybody rotation or mainly arm rotation is not as powerful as a swing thatuses the entire kinematic chain. The body should contribute about 40% to50% of the total rotational speed. There may be some variation due toindividual style, but a value that is consistently outside this rangeusually indicates a poor kinematic sequence.

As the bat moves through the swing, the angle between the bat lever andthe body lever changes. An angle that reflects the relative orientationof the bat lever and the body lever is called the hinge angle. In theillustrative embodiment shown in FIG. 20 , the hinge angle 2004 is theangle between the bat lever 2002 and the tangent 2003 that isperpendicular to the body lever 2001 in the two-lever mechanical model.Hinge angle is negative when the tip of the bat is angled toward thebody and positive when the tip is angled away from the body.

One or more embodiments may incorporate a method of calculating a commitevent. The commit event, also known as wrist release, occurs when thehinge angle is “released”. In other words, the moment when the hingeangle starts to move in a positive direction away from the body. Commitis the transition point in the kinematic chain between body-only motionand the wrist snap contribution. A batter begins the swing with the batangled towards the body. At commit, this hinge angle is released and thewrist is snapped forward to add speed to the bat and to contact theball.

FIG. 21 illustrates a method of calculating a commit event that may beused in one or more embodiments. The hinge angular velocity 2102 may befound by taking the first derivative of the hinge angle time series2101. Any desired method may be used to calculate or estimate aderivative; for example, one or more embodiments may use a centered,five-sample window to reduce sample noise. The commit event 2104 may bedefined as the instant when the hinge angular velocity 2102 exceeds athreshold value 2103 prior to impact. For example, a threshold value of60 rpm (360 dps) is illustrated in FIG. 21 .

One or more embodiments may define a sequence of events through a swing,and may derive one or more metrics from these events. FIG. 22 shows anillustrative swing with events annotated at the point in the swing whenthey occur. Event 2201 is the start of the downswing of the swing. Startof downswing indicates the start of significant motion of the downswing.An illustrative algorithm that may be used in one or more embodiments tocalculate the start of downswing is as follows. Start of downswing iscalculated by looking at the gyro xy resultant time series. Startingfrom the peak value, work backwards one sample at a time. For eachsample, fit a straight line through the peak value and the sample ofinterest. Find the moment in time where this straight-line approximationcrosses through zero angular velocity. This is an estimate of the startof downswing. Repeat this for every sample until the angular velocity ofthe sample of interest is less than 10% of the peak value. Keep thelatest start of downswing estimate that was found during this search.This start of downswing algorithm uses the xy resultant, which is abetter proxy for overall bat motion than, for example, using only the ycomponent of motion. The model-based algorithm also provides moreconsistent estimates than a threshold-based or zero-crossing algorithm.By fitting a model to the overall shape of the angular velocity curve,the algorithm ignores meaningless hand motion near the start ofdownswing, where the signal is on the same order of magnitude as thenoise. In one or more embodiments, the angular velocity curve isdecomposed into two additive components, body lever and bat lever, and ametric is derived therefrom and optionally reported to the user and/orutilized for internal calculations. In some embodiments, other metricsmay also be reported including measuring and comparing two parts (bodyand bat rotation) and utilizing peak speed ratios, amount of rotationratios, peak angular velocity ratios, centripetal acceleration, i.e.,how quickly a user starts accelerating a bat through body rotation toform metrics. Another metric may be formed by dividing peak hand speedby peak bat speed or an average of the hand speed and bat speed fromcommit to impact to reduce variability in the measurement. In one ormore embodiments, any of these metrics or any other metrics definedherein may be provided to the user through sound, for example if over,equal to, or under a predetermined threshold, or via a visual display,or AR/VR/MR display (or through both audio and visual) to provide theuser with biofeedback for use by the user to observe and/or alterposition, posture, swing.

Commit event 2014, also known as wrist release, occurs when the hingeangle is released, as described with respect to FIG. 21 .

The on-plane event 1803 occurs when the sweet spot approaches to withina threshold (such as three inches, for example) of the swing plane, asdescribed with respect to FIG. 18 .

For a swing that hits a ball, impact event 1804 occurs when the bat hitsthe ball and when this impact is detected by the sensor or sensors. Oneor more embodiments may also detect a virtual impact event even when thebat does not hit a ball (for example, for an “air swing”), as describedbelow.

For embodiments with an accelerometer, a simple impact detection may beperformed by searching for a large discontinuity in accelerometerreadings, corresponding to the shock of the impact. However, certainbatters generate accelerometer noise greater than 4 g prior to trueimpact. This has been observed in internal testing and in pro-levelswings. Analysis shows that this noise is almost always associated withhigh bat roll (z-axis angular velocity). Presumably, the bat is slippingin the grip, and the noise is caused by friction of the bat against thehands or gloves. Therefore, in one or more embodiments, the impactdetection algorithm may use both the gyro and accelerometer to detectimpact. The gyro search detects impact energy that is spread out overone or more subsequent samples. Searching forward, keep a running sum ofthe maximum gyro x, y, or z discontinuity. Reset the sum to zero if thediscontinuity drops below 540 dps and remember that sample. Stopsearching if the total discontinuity exceeds 1040 dps. The gyro-onlyimpact is the last sample that was remembered.

Starting from the gyro-only impact sample, search backward until theaccelerometer x, y, or z discontinuity is less than a threshold (80% ofthe saturation value). Usually, this occurs zero or one samples prior tothe gyro-only impact, but sometimes it can more. Impact is defined asthe sample just before the accelerometer discontinuity.

In rare cases, there is insufficient energy in the gyro signal to detectimpact. In this case, impact is the defined as the sample just beforethe first accelerometer discontinuity that exceeds the threshold.

In one or more embodiments, air swings are supported by enabling an airswing version of the impact detection algorithm. If the system does notdetect an impact event, the baseball swing processor determines whetherthe swing is a valid air swing. The air swing detection algorithm mayfor example look for peaks in the gyro xy resultant and accelerometer zcomponent. A swing may be classified as a valid air swing if forexample: the gyro xy peak exceeds 500 dps; the accelerometer z componentpeak exceeds 4 g; and the two peaks occur within 100 ms. In the case ofa valid air swing, the time of the gyro xy peak may be used as a proxyfor the impact event in all subsequent calculations. Processing of airswings continues the same as for impact swings. All swings may beconsidered invalid if the air swing criteria are not met, even if thereis a valid impact signature.

Peak bat speed event 2202 occurs at the moment of maximum forward batspeed, which happens at or before the moment of impact. Peak bat speedis calculated using the forward bat speed time series. Working backwardsfrom impact, peak bat speed is located by finding the sample with thepeak value.

Average power generated during the swing may be calculated aspower=mass×speed×acceleration, where mass is the effective mass of thebat, speed is the bat speed at impact, and acceleration is the averageacceleration during the downswing (bat speed/time to contact). Power maybe measured in Watts. The more mass the batter accelerates to highspeed, the higher the power.

Based on the start of downswing event 2201 and the impact event 1804, atime to contact metric may be calculated as the elapsed time betweenstart of downswing and impact. The clock starts when there is sufficientdownswing motion and ends when the bat contacts the ball (or at acorresponding virtual impact event for an air swing). Time to contactmeasures the total time it takes to complete a swing. A major leaguefastball takes about 400 milliseconds from pitcher to home plate. Inthat time, the batter must recognize the pitch, decide whether tocommit, and execute the swing. The quicker the time to contact, the moretime the batter has to recognize and commit to good pitches. The idealtime to contact depends on age, strength, bat length and weight,experience level, and swing style. Our testing shows the typical time tocontact for different age groups and skill levels: Little League:230-400 milliseconds; Senior League: 185-325 milliseconds; High School:140-260 milliseconds; College/Pro: 100-200 milliseconds.

FIG. 22 also illustrates metrics related to the orientation of theswing. For example, axis of rotation 2204, which is perpendicular toplane 2203 spanning points on the hand trajectory and is through centerof rotation 1903, forms a body tilt angle 2205 with the vertical axis.The center of rotation is a point at the center of the arc traced by thehands and is usually near the body's center of rotation. The axis ofrotation is the axis that the body rotates around and is usually alignedwith the spine. The body tilt angle is the angle between the axis ofrotation and vertical. The body and bat should rotate around the sameaxis. A large difference between the swing plane tilt angle and the bodytilt angle is an indication of a disconnected swing. In an efficientswing, the swing plane tilt angle and body tilt angle should beclosely-aligned.

FIG. 23 shows an embodiment that provides bio-feedback to the user forsetting posture or position or swing or any combination thereof viasound or AR/VR/MR visual displays, that enables working on postures,positions, swings and detecting proper or improper postures, positions,swings or portions thereof and to improve power and/or efficiency and toenable rehabilitation. One or more embodiments of the invention mayinclude utilizing sound, e.g., via headphones 2302, or at least oneVirtual Reality (VR), Augmented Reality (AR) or Mixed Reality (MR)display, glasses or goggles 2301 to provide bio-feedback to the user. Inone or more embodiments the audio and/or image components 2301 and/or2302 may be coupled with or formed into a helmet, such as a batter'shelmet for example. This enables the user to see the pitch approach,wherein the headset tracks the ball coming to provide metrics, and afterthe ball is hit, the system provides the user with the hitting metricsand/or a 3D tracer overlay, for example of the swing. MR is alsoreferred to as “hybrid reality” and includes use of real and virtualdata to produce novel environments and visual displays that include realand computed objects and interact, which also may include real-timedisplay of data. For example, in one or more embodiments, a sound orvisual display may be utilized to provide feedback to the user toindicate a correct position, or movement has been achieved. This enablesa user to work on portions of a swing or an entire swing using differentbody positions, for example to simulate different feet positions in asand trap for a golf swing for example and obtain feedback regarding theposition and/or swing using sound or visual feedback. In addition, byproviding metrics regarding the body position, body movement, piece ofequipment position, piece of equipment movement or any combinationthereof, embodiments of the invention enable a user to work ondeveloping more power and improving skills in a bio-feedback environmentand/or combine environment. Embodiments of the system also enablerehabilitation and general training of the body based on the datagathered by the system to suggest areas of the body to strength orstretch to improve the range of motion to avoid injury through use ofcorrect biomechanics.

One or more embodiments of the invention may include components thatenable calculation of various swing quality metrics for a swing of abaseball bat, softball bat, or other equipment. Based on extensiveanalysis of swing data and swing biomechanics, the inventors haveidentified three swing quality metrics that appear to be valuablehigh-level summaries of how effectively a user swings a bat. One or moreembodiments may extend or modify these three swing quality metrics inany desired manner. The three swing quality metrics described below arerotational acceleration, on-plane efficiency, and body-bat connection. Asystem that calculates these metrics is illustrated in FIG. 24 . User101 swings a bat 102 to hit a ball. An inertial sensor 104 is installedon bat 102. The sensor 104 may include for example a three-axisaccelerometer and a three-axis gyroscope. Data 2401 may be transferredfrom inertial sensor 104 to a processor 2400, for example over a networkconnection. The processor may be for example a mobile device such as asmart phone or a laptop, or any other computer such as a desktop orserver computer. In one or more embodiments the processor may be anetwork of multiple processors. In one or more embodiments the processoror a portion of the processor may be integrated into the inertial sensor104.

Embodiments of the invention may not include all of the components shownin FIG. 24 . For example, one or more embodiments may not include theinertial sensor 104, but may instead receive data 2401 generated byanother inertial sensor or similar device. One or more embodiments ofthe invention may not include processor 2400, but may include softwarethat executes on this processor to analyze data 2401.

Data 2401 may include a time series of acceleration data captured by anaccelerometer, and a time series of angular velocity data captured by agyroscope. The accelerometer and gyroscope may have three axes, and thetime series may each have three sub-series for each of the three axes.Processor 2400 may also access a bat geometry definition 2402, which mayfor example describe physical characteristics of the bat 102. Based onthe acceleration and angular velocity time series 2401, and the batgeometry 2402, the processor or processors 2400 may execute one or moresteps 2403 to calculate one or more swing quality metrics 2404. Thesemetrics may include any or all of rotational acceleration 2411, on-planeefficiency 2412, and body-bat connection 2413. The swing quality metrics2404 may include other metrics in addition to these three metrics, or asubset of the metrics shown. Data and metrics from multiple batters maybe captured in a database 2421, and analytics 2422 may be generated fromthis database. These analytics may for example be used to optimizebatting orders, to improve individual players' swings, to assignexercise programs, to assist with recruiting, to match players tocoaches, or to plan pitching strategies or adjustments.

One or more embodiments may have or use sensors instead of or inaddition to inertial sensor 104 on bat 102. For example, FIG. 24 showsoptional inertial sensor 104 a on one of the hands of batter 101, forexample in a batting glove; this sensor may capture data on motion ofthe hands. Sensors may be installed on any part or parts of the batter'sbody or on or in any equipment, such as on a belt, cap, or shoes. Datafrom these sensors may be fused with data from bat sensor 104 to analyzeand characterize the swing.

FIG. 24A shows an embodiment of the invention that uses video cameradata instead of inertial sensor data to track the motion of the bat. Thesensors of FIG. 24 (inertial) and FIG. 24A (video) are illustrative; oneor more embodiments may obtain bat motion data or motion data on otheritems such as the batter's hands using any type or types of sensors,including but not limited to inertial sensors and video camera sensors.Sensor data from any sensor or sensors may include or may be transformedto acceleration and angular velocity data 2401, which in turn may beused to calculate swing quality metrics.

In FIG. 24A, three video cameras 2431, 2432, and 2433 capture images ofthe swing of bat 102 by batter 101. One or more embodiments may use anynumber of video cameras. A potential benefit of using multiple camerasit that the bat may be visible at any point in the swing from at leastone camera. In this illustrative embodiment, no sensor or marker isplaced on bat 102 (or on player 101). Although markers may facilitatemotion tracking using video images, in some situations they may beawkward or time-consuming to use; therefore, one or more embodiments mayuse markerless motion tracking using analysis of video images onlywithout markers. Video streams from cameras 2431, 2432, and 2433 arecombined into image sensor data 2435, which consists of a time sequenceof frames from each camera. These frames 2435 are input into a step 2440that generates the bat acceleration and angular velocity time series2401 by analyzing the changes in the images over time. Techniques fortracking objects in video frames without markers are known in the art,as are techniques for generating data such as acceleration and angularvelocity from the tracked object positions in frames. These techniquesare used for example in markerless motion capture systems that recreate3D motion from a series of 2D video streams, without attaching markersto the objects of interest. Image processing and recognition techniquesmay be used for example to identify the bat (or portions of the bat thatare visible) in each frame, and stereo or multi-view triangulation maybe used to recover 3D positions of the bat's points from the 2Dprojections of the bat in each frame.

Step 2440 of calculating acceleration and angular velocity from thevideo frames 2435 may be performed by processor or processors 2400, orby any other system or systems. For example, in one or more embodimentsthe cameras 2431, 2432, and 2433 may perform all or part of thisprocessing internally. Processor 2400 may either obtain acceleration andangular velocity data 2401 directly from a sensor, or it may calculatethis data from one or more sources of sensor data from one or moresensors of any type or types. Sensor data in this context may representany data that represents or reflects motion of any object, including butnot limited to inertial sensor data, video camera frames, orcombinations thereof. One or more embodiments may combine data frominertial sensor 104 and cameras 2431, 2432, and 2433 (or otherarrangements of one or more cameras) and may perform sensor fusion tocalculate data 2401.

In one or more embodiments of the invention, sensor measurements,metrics and calculations such as those illustrated in FIGS. 24 and 24Amay be applied to movements other than the swinging of a bat. Forexample, without limitation, calculation 2403 of quality metrics 2404from inertial or video data may be applied to movements such as a golfswing, a tennis racket swing, a hockey stick shot, a lacrosse stickshot, or to movements without stick-like equipment such as a basketballshot, a soccer shot, a volleyball hit, a jump, a spin of a figureskater, or a baseball pitch or throw. Any type of motion may be analyzedwith respect to a natural plane of rotation for that motion or an axisof rotation for the motion. The quality of the motion may be summarizedin one or more quality metrics, such as metrics that capture theacceleration of the motion, the connection between the body of theperson performing the motion and any equipment or other body partsinvolved in the motion or between different body parts involved in themotion, and the efficiency of the motion with respect to the naturalplane for the motion. As an example, connection metrics for a spin of afigure skater may measure how the skater extends his or her arms or legsduring the spin, or how the arm and leg positions relate to each otheror to the body orientation. Quality metrics may be calculated frominertial sensor data or data from any other sensor on equipment or onthe user's body, or they may be calculated from analysis of videocaptured during the motion. In one or more embodiments, metrics andcalculations may also measure the stress on one or more joints of theuser during the motion; these stresses may be related to the motionquality metrics since efficient motions may generate less stress on thejoints.

An illustrative bat geometry definition 2402 is shown in FIG. 25 . Thisbat geometry includes the location of a hand position 2501 on the bat102, and a position of a sweet spot 2502 on the bat 102. These positionsmay be located for example along the longitudinal axis 210 of the bat.Positions may be measured for example relative to a position 2500 of theinertial sensor 104 on the bat. In one or more embodiments the positions2501 and 2502 may be set to any convenient locations; they may or maynot match actual hand positions of a specific real batter or a physicalsweet spot position of a bat. They may be set to average values ortypical values, for example. Typically, but not necessarily, the handposition 2501 may be near the knob end of bat 102, and the sweet spotposition may be at or near a position that is an optimal spot on the batfor contacting a ball. An optimal position for contacting a ball maycorrespond for example, without limitation, to a position that maximizesenergy transfer, a position that maximizes ball speed, or a positionthat minimizes vibration when the bat hits the ball at this positionalong the longitudinal axis 210. The bat geometry definition 2402 or anyportions of this definition may be for example stored in memory on theinertial sensor 104, or it may be stored in any memory accessible to theprocessor such RAM, ROM, or a hard disk containing a file or database. Asimple bat geometry definition file may contain for example only twonumbers: the distance between points 2501 and 2500, and the distancebetween points 2502 and 2500.

One or more embodiments may perform several preliminary calculationsbefore or during the generation of swing quality metrics. FIGS. 26 and27 show illustrative calculations that may be performed in one or moreembodiments. In FIG. 26 , the acceleration and angular velocity timeseries 2401 obtained from the inertial sensor or derived from cameraimage data may be integrated in step 2610 to determine the position andorientation of the sensor over time. Furthermore, the bat geometry 2402may be used to calculate the position and orientation over time of thebat and of specific points on the bat. For example, the processor of thesystem may calculate a trajectory of the longitudinal axis of the bat2603 at points in time through the swing. It may calculate a trajectory1901 of the hand position on the bat at points in time through theswing. And it may calculate a trajectory 1601 of the sweet spot positionon the bat at points in time through the swing. FIG. 26 shows anillustrative state of the bat at time 2604 in the swing, with batlongitudinal axis 210 k, hand position 2501 k, and sweet spot position2502 k at this time. The system may determine specific events ofinterest in the swing and may locate points in time in the sensor datatime series 2401 that correspond to these events. In particular thesystem may perform step 2611 to locate the impact of the bat with a ballor other object, to find impact time 502.

FIG. 27 illustrates how the data calculated in the steps shown in FIG.26 may be used in one or more embodiments to calculate swing qualitymetrics. The acceleration and angular velocity time series 2401, theimpact time 502, the hand position trajectory 1901, the sweet spotposition trajectory 1601, and the bat longitudinal axis trajectory 2603may be analyzed in calculations 2403 to generate metrics 2404.Additional inputs to the calculations 2403 may include the swing plane1701, and the body tilt axis 2204, which are described above withrespect to FIG. 17 for the swing plane, and with respect to FIGS. 19 and22 for the body tilt axis.

FIGS. 28 through 36 describe how the data shown in FIG. 27 may be usedin one or more embodiments to calculate the illustrative swing qualitymetrics shown in 2404: rotational acceleration, on-plane efficiency, andbat-body connection.

Turning first to rotational acceleration, one or more embodiments mayseparate a swing into a loading phase at the beginning of the swing, anda rotational phase when the batter completes the swing and acceleratesto hit the ball. One method that may be used in one or more embodimentsto define these two phases is to use the acceleration along the bat'slongitudinal axis. This approach is illustrated in FIG. 28 . Thelongitudinal axis 1501 of bat 102 is oriented so that the positivedirection from the knob of the handle towards the barrel. Anaccelerometer on the bat may measure acceleration in this longitudinaldirection, either directly if an axis of the accelerometer is alignedwith this longitudinal axis 1501, or indirectly along multiple axes. Ina typical swing, the batter adjusts the bat orientation in a loadingphase, and then swings in an approximately circular motion. The circularmotion results in centripetal acceleration along the longitudinal axis,which corresponds to a negative acceleration. FIG. 28 shows a plot ofacceleration 2801 along the axis 1501. At time 2803 this accelerationchanges sign, and it stays negative until impact 502. The phase 2802 ofcentripetal (negative) acceleration may be used to define the rotationalphase of the swing. The point 2803 corresponding to the sign change maybe used to define the transition between the loading phase of the swingand the rotational phase of the swing.

One or more embodiments may define a start of a centripetal accelerationphase in any desired manner, including but not limited to defining it asa zero crossing such as point 2803 in FIG. 28 . In one or moreembodiments, the start of centripetal acceleration event may bedetermined based on a model of the rotational patterns of a swing. FIG.29 illustrates a technique for defining the start of centripetalacceleration that may be used in one or more embodiments. A threshold2904 may be defined to locate points on longitudinal acceleration curve2801 that are relatively small compared to the peak centripetalacceleration 2901. For example, the threshold may be set to 10% of thepeak centripetal acceleration. For every sample starting at thisthreshold value and working backwards in time, a straight line may befit through the peak centripetal acceleration point 2901 and the sample.The time when this line crosses zero acceleration may be used as anestimate of the start of centripetal acceleration. This is illustratedin FIG. 29 for sample 2902; the line through points 2901 and 2902intersects the zero-acceleration axis at time 2903. Point 2903 maytherefore be used as an estimate of the start of centripetalacceleration. In one or more embodiments this process may be repeatedfor different samples working back in time until the accelerationmagnitude of the sample is less than a smaller threshold value, such asfor example 1% of the peak centripetal acceleration, and the latest timeof the intersection of the line through the sample may be used as thestart of centripetal acceleration. This procedure may generate a startof centripetal acceleration that is at or near the point in time whenthe centripetal acceleration changes sign.

Having identified a start of centripetal acceleration event, one or moreembodiments may calculate a rotational acceleration swing quality metricby measuring the centripetal acceleration at a specific time offsetafter this event. This calculation is illustrated in FIG. 30 . A timeinterval 3001 is fixed, and the point 3002 on centripetal accelerationcurve 2801 is located at this time interval after the start ofcentripetal acceleration 2903. The acceleration difference 3003 betweenthe centripetal acceleration at 3002 and the centripetal acceleration attime 2903 may be used as a rotational acceleration metric. The timeinterval 3001 may be fixed so that comparisons of rotationalacceleration across players measure how rapidly each player is able toaccelerate the swing over a common period of time.

This rotational acceleration metric 3003 is a measure of how the hitteraccelerates the bat into rotation. In one or more embodiments, it may bemeasured early in the rotational phase of the swing to captureinformation about the coordination and control patterns of the athlete;measuring early in the swing may make this metric less susceptible toswing differences based on pitch location. For example, the timeinterval 3001 may be selected, without limitation, in a range between 10and 50 milliseconds, inclusive.

Rotational acceleration is a useful metric to separate hitters betweenlevels. Hitters with high rotational acceleration exhibit high-levelmovement patterns and proper sequencing of segments through the swing.This is due in large part because it is simply not possible to achievehigh values of rotational acceleration without utilizing propersequencing to accelerate the bat into rotation. A high magnitude ofrotational acceleration is the result of proper timing and sequencing ofbat load as aggressive body rotation pulls the bat down into rotation.The higher the magnitude, the more functionally proficient the player isin accelerating the bat into a rotational path in a more dynamicallyadjustable swing. At elite levels, quickly and efficiently generatingenergy that can be transferred through the kinetic chain is essential tobe a successful hitter, given the incredibly dynamic and variable natureof the task.

FIG. 31 shows three illustrative swings 3101, 3102, and 3103. Swing 3101is from a power hitter who achieves early torso rotation. Swing 3102 isfrom a player who rotates the body less early in the swing, andtherefore achieves less power. Swing 3103 is from a player who primarilyuses the arms and hands rather than the body, and therefore has verylittle hitting power.

The major league baseball average for rotational acceleration isapproximately 17 g's. Elite hitters are consistently in the mid 20 g'swith some hitters reaching the 30 g's. Hitters with average rotationalacceleration values are often “block rotators”, that initiate rotationwith the hips and shoulders simultaneously. Hitters with low rotationalacceleration are commonly hand-dominant hitters who pull the knob of thebat with their upper body to initiate the swing.

Turning now to a second swing quality metric, on-plane efficiency, FIG.32 shows swing plane 1701 and a coordinate system that may be definedwith respect to the swing plane. This coordinate system consists of az-axis 1501 along the longitudinal axis of the bat, a y-axis 3202 normal(perpendicular) to swing plane 1701, and an x-axis 3203 orthogonal tothe y and z axes. (The labels x, y, and z for these axes are arbitrary;one or more embodiments may use any names or labels for any axes.)On-plane efficiency measures how much of the rotation of the bat isaround the y-axis 3202. Rotation around other axes does not contributeto the velocity at impact, which lies in the swing plane 1701.Therefore, a higher degree of on-plane efficiency reflects a moreefficient swing.

Angular velocity data from the inertial sensor on the bat may betransformed into the coordinate system of FIG. 32 . This transformationresults in three components of angular velocity: the y-axis angularvelocity 3212, which is the primary contributor to swing efficiency, thex-axis angular velocity 3213, and the z-axis angular velocity 3211. Thez-axis angular velocity 3211 is bat roll along the longitudinal axis ofthe bat, which is not a major factor in swing efficiency; however, alarge amount of x-axis angular velocity 3213 may reflect an inefficientswing.

In one or more embodiments, a rotation-on-plane ratio may be calculatedat any point in time during the swing as the ratio of the magnitude ofthe y-axis angular velocity 3212 to the magnitude of the vector sum ofx-axis angular velocity 3213 and y-axis angular velocity 3212. Thisratio is 100% for pure rotation around axis 3202; as more off-planerotation occurs around axis 3203, the ratio decreases. (Angular velocity3211 around the z-axis is ignored in this analysis because it istypically a minor factor.) An on-plane efficiency metric may becalculated as the value of this rotation-on-plane ratio at a point intime, or as an average over a period of time. In one or moreembodiments, the on-plane efficiency metric may be calculated as anaverage of the rotation-on-plane ratio between the start of centripetalacceleration and impact. This method is illustrated in FIGS. 33A and33B, which show x-axis and y-axis angular velocity for two illustrativeswings. Curves 3212 a and 3212 b show y-axis angular velocity for thetwo swings; curves 3213 a and 3213 b show x-axis angular velocity forthe two swings, and curves 3301 a and 3301 b show the magnitude of thevector sum of the x-axis and y-axis angular velocities for the twoswings. Curves 3302 a and 3302 b show the rotation-on-plane ratio 3310over time for the two swings. The values of the rotation-on-plane ratiosare averaged across the time interval 2803 (start of centripetalacceleration) to 502 (impact), giving average values 3303 a and 3303 bfor the two swings. The swing of FIG. 33A has a higher on-planeefficiency swing quality metric, since the y-axis angular velocity 3212a is a relatively larger fraction of the total xy angular velocity 3301a than the corresponding ratio for 3212 b and 3301 b.

On-plane efficiency measures how early a swing gets on plane and howwell it stays on plane as it approaches impact. In an efficient swing,the hitter wants to build as much forward bat speed on plane aspossible, to maximize functional bat speed at impact. Swinging the baton plane is one of the most important skills necessary to becoming ahigh-level hitter. It is also one of the most variable swing componentswhen comparing hitters. An efficient swing is one in which the hittergets the barrel on plane very early and deep in the swing path, whichallows them to better optimize acceleration of the barrel through thezone. Deviations from the swing plane are the direct result of changesin arm and wrist kinematics relative to the body rotations. The betterthe hitter is at minimizing these variable arm/wrist degrees of freedom,the longer the hitter's bat will be on plane. In a connected swing, thehitter will read the pitch early and make adjustments through the coreand the body instead of the arms and wrist in order to align the swingplane with the pitch location. A good functional swing will have anaverage on-plane efficiency starting at 70% or higher. A typical dynamicrange for on-plane efficiency is 65%-85%. Moving the on-plane efficiencymetric higher is desired and directly indicative of a more connectedswing.

Turning now to the body-bat connection swing quality metric, this metricmeasures the relationship between the hitter's body and the bat. Ideallythis relationship is approximately perpendicular throughout therotational portion of the swing. FIG. 34 illustrates a definition ofbody-bat connection that may be used in one or more embodiments. Thebody tilt axis 2204 may be defined from three points on the trajectoryof the hands, as discussed above with respect to FIGS. 19 and 22 . Thisaxis 2204 is calculated as a single axis for the entire swing. The batlongitudinal axis 1501 moves through the swing; therefore, the angle3401 between the body axis 2204 and the bat axis 1501 is a function oftime. This angle 3401 may be used as the body-bat connection metric atthat point in time, with an ideal value of 90°.

In one or more embodiments it may also be useful to calculate adisconnection metric, which is the complement of connection (theabsolute value of the difference between the body-bat connection angleand 90°). Disconnection is illustrated in FIGS. 35A and 35B. In FIG.35A, the connection angle 3401 a is greater than 90°, and thedisconnection angle 3501 a is angle 3401 less 90°. In FIG. 35B theconnection angle 3401 b is below 90°, and the disconnection angle 3501 bis 90° less angle 3401 b. Use of disconnection instead of connection maybe more useful when averaging or integrating connection angles overtime, since use of absolute differences prevents a negative differenceat one point in time from compensating for a positive difference at adifferent point in time.

As illustrated in FIG. 36 , one or more embodiments may measure thebody-bat connection (and/or disconnection) at the point of impact 502and at the start of centripetal acceleration 2803. The angle 3601between the axis 2204 and the bat axis 1501 a may be referred to as theearly connection or connection-early, and the angle 3602 between axis2204 and bat axis 1501 b at impact may be referred to as theconnection-at-impact. The connection-early and connection-at-impactvalues may be averaged to generate an overall body-bat connectionmetric, or equivalently the disconnection-early anddisconnection-at-impact values may be averaged to generate an averagebody-bat disconnection metric.

Connection is important measure of the athlete's ability to dynamicallyadjust for different pitch types and locations, as well as executingconsistent mechanics swing to swing. Connection and the relationshipbetween early connection and connection-at impact is also highly relatedto on-plane efficiency. In a good functional swing, the hitter adjuststo different pitch locations using their body tilt, keeping theirconnection values consistent. Hitters who adjust to different pitchlocations by manipulating the barrel with their hands will have variableconnection values across pitch locations. This introduces additionaldegrees of freedom at the wrist into the swing that are difficult tocontrol and execute with consistency.

The typical range for major league baseball players forconnection-at-impact is 80°-95°. Values for connection-early aretypically in the range of 75°-130°. High connection-early values (110°and greater) typically indicate a very steep vertical bat angle as thehitter begins to rotate. Hitters with connection-early values 110° andgreater will either need to correct their connection quickly as theybegin to rotate, or they will have poor on-plane efficiency values.Connection values ideally will not change based on pitch location andwill be consistently near 90° for all vertical bat angles. However,variable connection is common for hitters who manipulate the barrel withtheir hands. The bat axis orientation will change based on pitchlocation and the hitter should adjust their body tilt to match thatchange.

FIG. 37 shows the three illustrative swing quality metrics forhypothetical swings by three players. These metrics may be stored forexample in database 2421. The rotational acceleration 3701 and on-planeefficiency 3702 are calculated as described above. For bat-bodyconnection 3703, three values are shown: the early connection 3704, theconnection-at-impact 3705, and the average disconnection 3706.

In one or more embodiments of the invention, analysis of a swing mayinclude calculation of a rotational profile for the swing. Thisrotational profile may be calculated from sensor data captured by asensor attached to or integrated into a piece of equipment that is movedby a user, such as a baseball bat or a golf club. The illustrativeexamples described below show calculation of a rotational profile for abaseball swing, but one or more embodiments may calculate a similarrotational profile for any type of motion of a piece of equipment suchas a softball bat, cricket bat, tennis racket, golf club, hockey stick,or other equipment used in any type of activity.

The rotational profile as described below may provide information toanswer questions such as the following: How well does the user load? Howquickly can the user accelerate? What is the user's peak force? How muchforce does the user produce over the swing? How long does it take forthe user to produce that force? How well does the user sequence? How dousers compare?

FIG. 38 illustrates calculation of a rotational profile 3810 for a swingof bat 102 by user 101 to hit ball 103. The bat may have one or moresensors 104, which may include for example inertial motion sensors suchas 3-axis accelerometer 105 and 3-axis rate gyroscope 106. Sensor(s) 104may also include or be attached to a network interface 3801. In one ormore embodiments, the sensor device may include a processor and amemory. Data captured by sensors 105 and 106 during a swing may betransmitted to a processor 2400 over a network connection (which may bewired or wireless) for analysis. The processor may for example beinstalled in a mobile device 3802, such as a smartphone. In one or moreembodiments, processor 2400 may be a network of processors; for example,mobile device 3802 may forward data to one or more servers for all orpart of the analysis.

FIG. 38 shows illustrative calculation steps that may be performed byprocessor(s) 2400 to obtain rotational profile 3810 for a swing. Thesensor data 2401 captured during the swing may be analyzed in severalstages. A bat trajectory 301 may be calculated, as described above forexample with respect to FIG. 1 . This trajectory may include theposition and velocity of points on the bat at a sequence of times duringthe swing. Specific points on the bat that may be of interest mayinclude the position 1901 of the hands on the bat and the position 1601of the sweet spot (which may be selected as any convenient location onthe bat that is away from the hands, towards the barrel end of the batfor example). As described above with respect to FIG. 19 , a center ofrotation 1903 may also be calculated for the swing.

As described above with respect to FIG. 20 , using the center ofrotation 1903 and the position 1901 of the hands and position 1601 ofthe sweet spot, the swing may be analyzed using a two-lever model thattreats the motion of the bat as resulting from rotation of body lever2001 between the center of rotation and the hands, and rotation of thebat lever 2002 between the hands and the sweet spot. Motion of each ofthese two levers may be analyzed separately, which provides insight intothe rotational profile of the swing. For example, in an effective swing,the user typically begins with body rotation and then later in the swingthe user releases the wrists to move the bat lever so that the batcontacts the ball with high velocity.

The body lever 2001 and the bat lever 2002 rotate throughout the swing,as illustrated for example in FIG. 19 . A body rotation angle 3803 maybe calculated at each point in time as the angle between the body leverat that time and the initial body lever at the start of the swing. Ahinge angle 2004 may be calculated at each point in time based on therelative orientation of the bat lever and the body lever at that time;for example, as shown in FIG. 20 , the hinge angle 2004 may becalculated as the angle between the perpendicular 2003 to the body lever2001 and the bat lever 2002. In one or more embodiments, the bodyrotation angle and the hinge angle may be calculated in the swing plane;for example, the body lever and bat lever may be first projected ontothe swing plane and the angles may be calculated based on theseprojected levers.

The time rates of change of these angles 3803 and 2004 may form part ofthe rotational profile 3810. The body rotation rate 3804 at a point intime may be calculated as the instantaneous rate of change (the timederivative) of the body rotation angle 3803, and the bat rotation rate2102 may be calculated as the instantaneous rate of change of the hingeangle 2004. In one or more embodiments the bat rotation rate may becalculated as the rate of change of the absolute angle of the bat lever,rather than of the relative angle between the bat lever and the bodylever.

In one or more embodiments, the rotational profile 3810 may also includethe centripetal acceleration 2801 of the bat at each point in time,measured along the bat's longitudinal axis 1501, as illustrated forexample in FIG. 28 . This longitudinal axis may for example correspondto one of the axes of the accelerometer on the bat, or the accelerationvector may be projected onto this axis to calculate the centripetalacceleration. Centripetal acceleration may be oriented so that it ispositive when the acceleration is towards the tip of the bat, andnegative when the acceleration is towards the knob of the bat.

One or more embodiments of the invention may also include one or moreswing metrics 180 in the rotational profile 3810. These metrics 180 maybe calculated from sensor data 2401 or from any of the derived valuesshown in FIG. 38 or elsewhere in this application. They may include anyof the metrics described above. Some illustrative additional metricsthat may be calculated from the rotational profile curves 2801, 3804 and2102 are described below.

As described above with respect to FIG. 7 , in one or more embodimentsthe sensor data and derived values calculated from this data may bestored in a swing database 701. This database may contain values fromswings by multiple users, and analyses 720 may be performed on the datato compare and evaluate users' swing performance. As shown in FIG. 39A,these analyses may be performed by a computer (or network of computers)3901. In addition to the analyses illustrated in FIG. 7 , analyses 720may generate equipment fitting or equipment recommendation analyses 3902for the user 101. For example, these recommendations may include values3903 such as the recommended length, weight, shape, or materials of abat, or a recommended specific model 3904. These recommendations may forexample be transmitted to mobile device 3802 associated with user 101.The user 101 may for example take one or more swings, and sensor datatransmitted to mobile device 3802 may be forwarded to swing database 701for storage or analysis; equipment recommendations may then be sent backto the mobile device 3802 shortly thereafter so that the user receivesimmediate advice on optimal equipment. FIG. 39B shows anotherillustrative application of the analysis and fitting system of FIG. 39A.User 101 may take swings with multiple equipment options, such as bats3910 a, 3910 b, and 3910 c, to determine which of these optionsfunctions best for that user. Sensor data collected from each of thesebat options may be collected by device 3802 and analyzed by processor3901. For example, this analysis may generate a comparison table 3920that shows swing metrics 3921, 3922, and 3923 for swings from each ofthe bats 3910 a, 3910 b, and 3910 c. In one or more embodiments, anynumber of equipment options may be compared using any number of metrics.In this illustrative example, the reported metrics include bat swingspeed at impact 3921, the time of the swing (between start of swing andcontact) 3922, and the acceleration impulse 4305 (which is calculatedfrom the rotational acceleration curve of the rotational profile, and isdescribed below with respect to FIG. 43 ). Metrics may include forexample any values derived from acceleration or gyro data, or from therotational profile. Table 3920 also includes a combined score 3924 foreach bat, which may for example be a weighted sum (or any otherfunction) of the metrics 3921, 3922, and 3923. Bat 3910 b has thehighest combined score 3930, so this bat may be recommended to user 101.In one or more embodiments, users may be able to select one or moremetrics that are most important, assign weights, and compare batrankings on this basis.

FIG. 40 shows elements of an illustrative rotational profile 3810 a,including centripetal acceleration 2801 a, body rotation rate 3804 a,and bat rotation rate 2102 a. Each of these elements is a sequence ofvalues over time throughout the swing, shown in FIG. 40 as correspondinggraphs with the time axis 4001 normalized to a fraction of the totalswing duration. The shape of these curves may provide insights into thequality of the swing, and differences in curves across players may helpdifferentiate player performance and skill level. For example, FIG. 41Ashows centripetal acceleration curves for swings from players of fivedifferent skill levels. Curve 4101 is from a US Major League Baseball(MLB) “power hitter”; the peak (negative) centripetal acceleration ofthis player is lower (more negative) than the corresponding peak for theother players. Curve 4102 is from an MLB all-star. Curve 4103 is from anMLB top prospect. The curves with the highest (least negative) peakcentripetal acceleration are curve 4104 from a player with a highstrikeout rate, and curve 4105 from an MLB drafted player who was notsuccessful. In these examples there is a clear relationship betweenperformance and the centripetal acceleration curve of the rotationalprofile.

FIG. 41B shows body rotation rate and bat rotation rate curves forswings from players of three different skill levels. These curvesprovide indicators of how well the different players sequence theirmotions through the swing. Ideally the body should rotate first, withminimal change to the hinge angle, and then the bat should be releasedfor a rapid change in the hinge angle. Profile 4110 d shows a playerwith minimal bat-body sequencing; the bat rotation rate 2102 d increasesfrom the start along with the body rotation rate 3804 d. Profile 4110 eshows a player with moderate bat-body sequencing, and profile 4110 fshows a player with excellent bat-body sequencing. The inventors havefound that proper sequencing, as revealed by these rotational profilecurves, is closely correlated with higher (more negative) values forcentripetal acceleration as the player is effectively using the body toaccelerate the bat as opposed to initiating the swing with hand motiontowards the ball or wrist motions. For example, the average rotationalacceleration through the swing of 4110 d is 8.6 g, the averagerotational acceleration through the swing of 4110 e is 13.1 g, and theaverage rotational acceleration through the swing of 4110 f is 21.2 g,showing that the last player develops more power via excellentsequencing.

In one or more embodiments of the invention, analysis of swing data mayinclude partitioning the swing into phases. The timing of theses phasesmay provide insight into how a user sequences the different actions thatconstitute a complete swing. For example, in an efficient swing thebatter successively rotates the lower body, the upper body, and then thebat.

Illustrative phases are shown in FIG. 42 for a swing with centripetalacceleration curve 2801 a. (Phases may be calculated based on any sensordata or derived data, including but not limited to the centripetalacceleration.) A start of swing time 4201 may be defined or calculated,as well as an end of swing time 4202 (which may for example correspondto impact between the bat and the ball). Between the start 4201 and end4202, four swing phases 4211, 4212, 4213, and 4214 may be calculated.The load phase 4211 may start at the start of swing 4201 and may end forexample at point 4203 when centripetal acceleration 2801 a crosses thezero axis and changes from a positive value to a negative value. Theaccelerate phase 4212 follows the load phase, and is the phase whencentripetal acceleration changes rapidly. The peak phase 4213 followsthe accelerate phase, and corresponds to the bat unhinging from the bodyand accelerating from the body. The transfer phase 4214 follows the peakphase and continues to the end of swing 4202.

FIGS. 43 and 44 show illustrative swing metrics that may be calculatedfrom the centripetal acceleration and rotational rate curves, and fromthe phases illustrated above in FIG. 42 . One or more embodiments of theinvention may calculate any desired metrics from this data or from anyof the sensor data or other derived quantities. FIG. 43 shows fiveillustrative metrics 4301, 4302, 4303, 4304, and 4305 that may becalculated from the centripetal acceleration curve 2801 a. The peakloading acceleration 4301 may be calculated as the acceleration value atthe peak (positive) maximum point 4311 in the load phase. For theaccelerate phase, the rate of acceleration metric 4302 may be calculatedas the slope of the line segment between point 4203 at the start of theacceleration phase and the point 4312 at the end of the accelerationphase; this value 4302 also equals the average rate of change ofcentripetal acceleration over the accelerate phase. In the peak phase,the peak acceleration metric 4303 may be calculated as the accelerationvalue at the minimum (most negative) point 4313, and the time to peakforce metric 4304 may be calculated as the time difference between thestart of the accelerate phase and the time at the minimum point 4313. Asmaller time to peak force may give a player more time to react to anincoming pitch. The acceleration impulse metric 4305 may be calculatedas the integral of the centripetal acceleration curve across theaccelerate, peak, and transfer phases; this integral corresponds to theshaded area shown in FIG. 43 . This acceleration impulse metric may forexample be correlated with the total centripetal force produced duringthe downswing.

FIG. 44 shows three illustrative metrics 4401, 4402, and 4403 that maybe calculated from the body rotation rate 3804 b and the bat rotationrate 2102 b. The peak body rotation rate 4401 may be calculated as themaximum value during the swing of the body rotation rate, and the peakbat rotation rate 4402 may be calculated as the maximum value during theswing of the bat rotation rate. The rotation rate ratio 4403 may becalculated as the ratio of the peak bat rotation rate 4402 to the peakbody rotation rate 4401. One or more embodiments may include additionalmetrics calculated from the rotation rates, such as metrics that combinesequencing, timing, and peak data into a quality score, and metrics thatmeasure stability and balance.

The discussion above focuses primarily on the example of a baseball batswing to illustrate calculation and use of a rotational profile for apiece of equipment moved by a user. In one or more embodiments, the sameor similar features may be applied to movement of other types ofequipment, such as equipment used for other sports. The terms “battrajectory”, “bat lever”, “bat rotation rate”, “peak bat rotation rate”,etc. may be interpreted in one or more embodiments of the invention as“equipment trajectory”, “equipment lever”, “equipment rotation rate”,“peak equipment rotation rate” and so forth, for any type of equipment.

For many sports, a “swing” or other movement of a piece of equipment maybe analyzed using a two-lever model similar to the model described abovefor a baseball swing. This two-lever model may be used for example forequipment that is held by a user and that has a portion of the equipment(which may be called the “sweet spot”) that may strike or contact a ballor other object. The “body lever” may extend from a center of rotation(which may be a point on the user's body) to the position of the handson the equipment. The “equipment lever” may extend from the handposition to the sweet spot. The motion of the equipment may be viewed asa combination of a rotation of the body lever around the center ofrotation, and a rotation of the equipment lever relative to the bodylever at the joint of the hands. A rotational profile and variousmetrics may be calculated for this equipment motion using the devicesand techniques described above for a baseball bat swing.

FIG. 45 shows an example of calculating a rotational profile for a golfswing. Like the baseball swing examples described above, this exampleillustrates a general technique that may be used for any type ofequipment. In this embodiment of the invention, an inertial sensor maybe attached to a golf club to collect data when user 4501 swings theclub. Data may be transferred to and analyzed by one or more processors,as shown for example in FIG. 38 ; this data may be stored in a databaseand used for fitting or other analyses, as shown for example in FIGS.39A and 39B.

A two-lever model may be used to analyze the golf swing shown in FIG. 45with procedures that are similar to those described above for a baseballbat swing. A center of rotation 4504 may be calculated for all or aportion of the swing. A body lever 4507 may extend from the center ofrotation 4504 to the hand position 4503 on the golf club, and a clublever (a type of equipment lever) 4506 may extend from the hand position4503 to the sweet spot (on the club face) 4502 of the club, which may befor example any spot on the club that may be used to strike the golfball. The center of rotation 4504 may for example be calculated usingthree points 4511, 4512, and 4513 on the trajectory of the sweet spot,by locating the point coplanar with these three points and equidistantfrom each point; this method is analogous to the method shown in FIG. 19for a baseball bat swing.

In one or more embodiments of the invention, motion of a piece ofequipment may be analyzed in stages. For example, for the swing of thegolf club shown in FIG. 45 , path 4510 shows the trajectory of the sweetspot of the club in the downswing, and a different path 4514 shows thetrajectory of the sweet spot during the backswing. The downswing andbackswing may therefore have different centers of rotation 4504 and4515, respectively. Physically this may correspond for example to aweight shift to the front foot and forward translation of the golfer'scenter of mass that may occur during the first half of the downswing.Illustrative points on the downswing trajectory that may be used tocalculate center of rotation 4504 may be the point at impact, the pointat 75% of the time from the start of the downswing to impact, and thepoint at 87.5% of the time from the start of downswing to impact. Thestart of downswing may be defined for example as the point where themagnitude of the angular velocity of the clubhead along the planeperpendicular to the club's longitudinal axis is at a minimum. For thebackswing, illustrative points to determine center of rotation 4515 mayfor example include the point of peak clubhead angular velocity (alongthe plane perpendicular to the longitudinal axis), the point halfway (bytime) between the start of backswing and this peak angular velocitypoint, and the point halfway (by time) between the peak angular velocitypoint and the start of the backswing.

A rotational profile 4520 and various swing metrics 4524 may becalculated for a golf swing in a manner analogous to that describedabove for a baseball swing. For example, rotational profile 4520 mayinclude the curve 4521 of centripetal acceleration along the golf clublongitudinal axis (along the shaft), body rotation rate curve 4522 forthe rate of change of the angle of body lever 4507, and equipment (club)rotation rate curve 4523 for the rate of change of the “hinge angle”between body lever 4507 and equipment (club) lever 4506. Metrics 4524may be calculated from the rotation profile 4520 or from any sensordata; illustrative metrics that may be used for golf may include forexample, without limitation, the peak body rotation rate, the peakequipment (club) rotation rate, and the rotation rate ratio, defined forgolf as in FIG. 44 for baseball.

Returning now to the fitting system described with respect to FIGS. 39Aand 39B, in one or more embodiments of the invention this fitting systemmay enable a user to compare equipment performance using any metric ormetrics derived from sensor data captured during swings of differentpieces of equipment. FIG. 46 shows a variation of the embodiment shownin FIG. 39B; this embodiment combines metrics for acceleration, speed,and momentum to calculate a metrics score for each piece of equipmentused or tested. In this example, user 101 takes one or more test swingswith each of three different bats 3910 a, 3910 b, and 3910 c. Each ofthese bats is equipped with an inertial sensor during these swings. Anynumber of inertial sensors may be used to measure swings of thesedifferent bats. For example, each bat may be equipped with its owninertial sensor. Alternatively, as shown in FIG. 46 , a single sensormay be moved from one bat to a different bat to obtain sensor data forthis different bat. For example, bat 3910 c is equipped with inertialsensor 104 b. Bat 3910 a is initially equipped with sensor 104 a. Aftertaking test swings with bat 3910 a, user 101 (or a bat fitter or coach)may move sensor 104 a to bat 3910 b and then take test swings with bat3910 b. Regardless of which sensors are used on which bats, sensor datafrom swings of each bat may be captured and transmitted to a server 3901for analysis. Data captured by sensors 104 a and 104 b may betransmitted to a mobile device 3802, or to another local device such asan Internet gateway, and may be forwarded to server 3901.

In this example, server 3901 generates a metrics comparison table 4620with three metrics derived from the inertial sensor data captured bysensors 104 a and 104 b. Some or all of these metrics may also be afunction of the physical characteristics of the bats, such asillustrative characteristics 4605 for bats 3910 a, 3910 b, and 3910 c.Table 4605 shows values for bat lengths, weights, and moments of inertia(MOI); one or more embodiments may use these or any othercharacteristics of the bats to calculate any of the metrics 4620.Metrics may also be calculated on mobile device 3802, or by processorsin the sensors 104 a and 104 b, or by any combination of the sensorprocessors, the mobile device, and one or more servers; in one or moreembodiments any processor or combination of processors may calculatemetrics. These metrics describe three factors that contribute to thepower of a swing: an acceleration metric 4601, a speed metric 4602, anda momentum metric 4603. The acceleration metric 4601 may for exampledescribe how quickly or to what extent a user can accelerate each bat.The speed metric may for example describe how much speed the user cangenerate with each bat. The momentum metric may be valuable because itmay for example describe how much momentum the user can generate witheach bat to transfer power to a struck ball. FIG. 46 shows these metricswith respect to swings of a baseball bat; similar metrics may be usedfor any other type of equipment for any other sports or otheractivities.

In many situations there may be tradeoffs among these three factors ofacceleration, speed, and momentum. For example, a heavier bat 3910 b maybe more difficult to accelerate, but it may increase the momentumtransferred to a ball for a given speed. Similarly, a longer bat 3910 cmay increase speed for a given angular velocity because of the longerlever arm of the bat, but the increased rotational inertia of the longerbat may decrease rotational acceleration for a given applied torque. Avery strong player may for instance be able to effectively accelerateeven a heavy bat, while a weaker or younger player may develop morepower with a lighter bat, despite the reduction in momentum.

The recommended bat (or other equipment) for each player may thereforedepend on a combination of the three factors 4601, 4602, and 4603. Inone or more embodiments, processor 3901 may therefore calculate ametrics score 4610 that is based on all three of these factors. Theequipment with the highest metrics score may be recommended from amongthe equipment options that the user has tested. In the example of FIG.46 , bat 3910 c has the highest metrics score 4610 c, so this bat isrecommended. The metrics score 4610 may be calculated as any function ofthe metrics 4601, 4602, and 4603; other factors such as equipment orplayer characteristics may also be taken into account in thiscalculation.

FIG. 47 shows illustrative inputs and calculations that may be used toderive metrics score 4610 in one or more embodiments. The accelerationmetric 4601 may for example be based on the rate of centripetalacceleration 4302 during the “accelerate” phase of a swing, as describedwith respect to FIG. 43 . The acceleration metric 4601 may be aninstantaneous or average rate of change of centripetal acceleration atany point in time or over any time interval. (The metric 4302 is therate of change of acceleration during the accelerate phase, which is theaverage “jerk” during this phase. Because acceleration is a morefamiliar concept to most users than jerk, one or more embodiments maypresent this data as a change in acceleration—measured for example ing's—over a fixed time interval; this metric is proportional to metric4302 and contains the same information, since (A acceleration)=(averagejerk)*(time interval).) The speed metric 4602 may for example be basedon the speed of the “sweet spot” of the bat 506 (or of a similar pointon other equipment) at an appropriately determined swing endpoint (suchas impact), as described with respect to FIG. 5 . In one or moreembodiments, the speed metric may be based on the speed of the user'shands at the swing endpoint; hand speed is related to sweet spot speed(treating the equipment as a rigid body), but in some situations it maybe a more convenient or natural speed measure. The momentum metric 4603may for example be calculated as a product of end speed 506 and aneffective mass 4711 of the equipment. This effective mass may reflecthow much of the mass of the equipment may affect a struck ball or otherobject at impact, which may depend for example on the shape and massdistribution of the equipment. An illustrative calculation of effectivemass that may be used for baseball bats or similar equipment may be forexample to multiply the total mass 4712 of the bat by a factor 4713,which for illustration may be 0.75. Other types of equipment may haveother factors 4713 or functions that derive an effective mass 4711 fromthe equipment mass 4712.

These inputs 4302, 506, and 4711 are illustrative; one or moreembodiments may define and calculate acceleration, speed, and momentummetrics with other techniques. These metrics may be derived from any ofthe sensor data captured during the swings of different equipmentoptions, and from any characteristics of the equipment such as the sweetspot location, the mass and mass distribution, the effective mass, andthe location of the longitudinal axis or other axes.

In one or more embodiments of the invention, some or all of these inputsmay then be scaled in step 4715 to form the acceleration, speed, andmomentum metrics 4601, 4602, and 4603. This scaling may be linear ornonlinear. An illustrative scaling method may for example scale data sothat the highest observed value of each metric (across the testedequipment options) is set to a “perfect score” (such as 10), and pointsare subtracted at some rate for deviations from this highest value. Forexample: the acceleration metric 4601 may be reduced by 1 point for each0.5 g/s below the highest acceleration value; the speed metric 4602 maybe reduced by 1 point for each mph below the highest speed value; andthe momentum metric may be reduced by 1 point for each 0.75 kg-m/s belowthe highest momentum value.

The (potentially scaled) metrics 4601, 4602, and 4603 may then becombined to form a metrics score 4610. The metrics score 4610 may becalculated as any linear or nonlinear function of these inputs 4601,4602, and 4603. An illustrative method for combining these metrics is toform a weighted sum of the individual metrics, using weights 4701, 4702,and 4703 for metrics 4601, 4602, and 4603, respectively. These weightsmay be selected by a user or by an expert, or they may be based onempirical analysis of what weights best correlate with observedperformance.

FIG. 48 shows an illustrative example of metrics calculated from swingsof three different bats by two different players. For ease ofillustration, this example shows only the acceleration metric 4601 andthe speed metric 4602; in one or more embodiments a momentum metric mayalso be used to select an optimal bat for each player. Each playerswings each of the three bats four times, and data are collected andanalyzed for each swing. Plot 4801 a shows the speed and accelerationmetrics for the first player, and plot 4801 b shows the speed andacceleration metrics for the second player. The combination of speed andacceleration shows a “power profile” for each player with each bat.Points are labelled using legend 4806 to show which bat was used foreach swing. Maximum power results from a combination of high speed andhigh acceleration; thus the “power zone” 4805 that players may target isthe upper right zone of the plots.

Plot 4801 a for the first player shows that the grouping 4802 a of swingmetrics associated with bat 3 are closest to the power zone 4805. Forthe second player, grouping 4802 b of metrics associated with bat 1 areclosest to the power zone. Therefore, the fitting system makesrecommendations 4810 with optimal bats for each player (from among thosetested).

In one or more embodiments of the invention, additional or alternativemetrics scores or metrics combinations may be used to assess otheraspects of performance and to fit equipment for other objectives. Forexample, in baseball, power is a key objective but effective contactwith the ball is also an objective. FIG. 49 shows another analysis ofsensor data that may for example be used to identify a bat that is bestfor this contact objective for a particular player. The metrics used forthis analysis include on plane efficiency 2412 and the attack angle1602. An optimal contact zone 4905 requires a high on plane efficiency,and an attack angle within a target range. For this player, bat 3appears to provide the best contact performance. One or more embodimentsmay combine metrics in any desired manner to score the effectiveness ofequipment for any type of objective, and different equipment may beoptimal for different objectives.

In one or more embodiments, a metrics score may be combined with otherfactors to recommend a piece of equipment. FIG. 50 shows an examplewhere metrics score 4610 is combined with a user feel score 5002, anexpert opinion score 5004, and a consumer comparison score 5006, togenerate an overall score 5001 for each piece of equipment tested. Thesefactors 5002, 5004, and 5006 are illustrative; one or more embodimentsmay combine metrics data with any other information to generateequipment recommendations.

The user feel score 5002 may for example be based on input 5003 from theuser reporting how the user subjectively felt each piece of equipmentperformed. The expert opinion score 5004 may be based on inputs 5005from one or more experts who test or review the equipment options. Theconsumer comparison score 5006 may be based on data 5007 collected fromconsumer purchases, consumer ratings, or from sensor data from a pool ofconsumers that have used the equipment. In one or more embodiments ofthe invention, fitting recommendations may compare a user's data to adatabase of swing data from other users to identify other users thathave similar swing styles, or who are similar to the user based on usercharacteristics such as age, height, gender, weight, position played,and years of experience. This database may also have information on theequipment used by these other users, and on ratings of equipment optionsfrom those other users. The fitting recommendations for the user may forexample include equipment that is used by or recommended by these othersimilar users.

The user feel for a bat may be for example related to measurable batcharacteristics such as the bat's length, weight, and moment of inertia(or other measures of mass distribution). Therefore, if a user indicatesthat the user feel score for a particular tested bat is best, one ormore embodiments may search for similar bats with similarcharacteristics such as length, weight, and mass distribution, and mayrecommend that the user consider these similar bats as well. Similarly,any other measurements (quantitative or qualitative) or comparisons of abat's performance for a user may be related to these batcharacteristics, and one or more embodiments may search a database tofind bats that match the length, weight, weight distribution (such asmoment of inertia), or any other bat characteristics in order toidentify bats to recommend to the user.

The four factors 4610, 5002, 5004, and 5006 may be combined into anoverall score 5001 for each piece of equipment. These factors may becombined using any linear or nonlinear function. FIG. 50 shows anillustrative method of combining these factors that calculates theoverall score 5001 as a weighted sum of the inputs. In this example, theuser may provide input 5010 that is used to generate weights 5009; thismethod gives the highest weight to the factor or factors that the userindicates are most important.

In one or more embodiments, the user may view the individual factorsthat contribute to an overall score for each piece of equipment, and maymake his or her own determination as to which combinations of factorsare optimal, without relying exclusively (or at all) on the aggregatedscore. For example, a user may determine that the desired equipmentshould be the option that is associated with the highest speed metric,as long as the momentum metric is above some threshold value. Users mayview the individual metrics associated with each piece of equipment aswell as the other factors such as expert and consumer scores and theuser's subjective feel scores, and may select equipment that combinesthese factors in any desired manner.

Some of the metrics discussed above, such as the speed metric 4602, maydepend on defining and identifying an endpoint in a swing; for example,the speed of the sweet spot of the equipment at this endpoint may beused as the speed metric. In many cases the natural endpoint of a swingis the point of impact, such as when a baseball bat hits a baseball.However, particularly when fitting and testing equipment, a user may notalways be able to generate an impact. Instead, the user may take “airswings” (without an impact) to test the feel and performance of theequipment. In these situations, one or more embodiments of the inventionmay define a different endpoint that serves as a “virtual impact” pointfor purposes of calculating metrics. FIGS. 51A and 51B illustrate thisissue. In FIG. 51A, user 101 a swings a bat 102 a and hits ball 103.Curves 5101 a and 5102 show the magnitude of the acceleration andangular velocity, respectively, measured by the accelerometer and gyroon the bat. The impact point 5103 is easily identified by the shockmeasured by the accelerometer, and this impact is used as the swingendpoint 5110 a. In the example shown in FIG. 51B, user 101 b swings bat102 b without any impact. Acceleration magnitude and angular velocitymagnitude curves 5101 b and 5102 b therefore show no signature of ashock. As a proxy for impact, one or more embodiments may use the point5110 b where the angular velocity magnitude (or the magnitude of any ofthe components of the angular velocity vector) is at a maximum; thuspoint 5110 b may be used as the endpoint for this swing. All othercalculations described above that use the point of impact may use thisendpoint 5110 b for this swing instead.

While the ideas herein disclosed has been described by means of specificembodiments and applications thereof, numerous modifications andvariations could be made thereto by those skilled in the art withoutdeparting from the scope of the invention set forth in the claims.

What is claimed is:
 1. An equipment fitting system that compares swingmetrics, comprising: one or more inertial sensors, wherein each inertialsensor of said one or more inertial sensors comprises an accelerometer;a gyroscope; and a network interface; each inertial sensor is coupled toone or more pieces of equipment of a plurality of pieces of equipmentused by a user; each inertial sensor is configured to capture inertialsensor data at a sequence of times during a swing of each piece ofequipment of said one or more pieces of equipment to which said eachinertial sensor is coupled; a processor coupled to said one or moreinertial sensors via a network connection, wherein said processor isconfigured to receive said inertial sensor data associated with saidswing of each piece of equipment of said plurality of pieces ofequipment; for said each piece of equipment, calculate swing metricsbased on said inertial sensor data, said swing metrics comprising anacceleration metric; a speed metric; and a momentum metric; andcalculate a metrics score from said swing metrics; and, recommend anoptimal piece of equipment of said plurality of pieces of equipment forsaid user based on said metrics score.
 2. The equipment fitting systemof claim 1, wherein said processor is further configured to calculatesaid metrics score as a weighted sum of said swing metrics.
 3. Theequipment fitting system of claim 1, wherein said recommend said optimalpiece of equipment is further based on one or more of a user feel scoreprovided by said user for said each piece of equipment; an expertopinion score provided by one or more experts for each piece ofequipment; and, a consumer comparison score provided by one or moreconsumers for each piece of equipment.
 4. The equipment fitting systemof claim 3, wherein said processor is further configured to calculate anoverall score for said each piece of equipment based on said metricsscore; said user feel score; said expert opinion score; and saidconsumer comparison score; and, select said optimal piece of equipmentas a piece of equipment having a highest overall score.
 5. The equipmentfitting system of claim 4, wherein said processor is further configuredto calculate said overall score as a weighted sum of said metrics score;said user feel score; said expert opinion score; and said consumercomparison score.
 6. The equipment fitting system of claim 5, whereinsaid processor is further configured to obtain or calculate weights forsaid weighted sum based on input from said user.
 7. The equipmentfitting system of claim 1, wherein said each piece of equipment is abat.
 8. The equipment fitting system of claim 1, wherein said each pieceof equipment is a golf club.
 9. The equipment fitting system of claim 1,wherein said each piece of equipment of said plurality of pieces ofequipment is associated with a longitudinal axis; a sweet spot position;and an effective mass.
 10. The equipment fitting system of claim 9,wherein said momentum metric equals said effective mass times said speedmetric.
 11. The equipment fitting system of claim 10, wherein said eachpiece of equipment is a bat; and, said effective mass comprises 0.75times a mass of said bat.
 12. The equipment fitting system of claim 9,wherein said speed metric comprises a speed of said sweet spot positionat an endpoint of said swing.
 13. The sequipment fitting ystem of claim12 wherein said endpoint of said swing comprises a time of said sequenceof times of an impact between said each piece of equipment and anobject.
 14. The equipment fitting system of claim 12 wherein saidendpoint of said swing comprises a time of said sequence of times when arotational velocity magnitude of said each piece of equipment ismaximum.
 15. The equipment fitting system of claim 9, wherein saidacceleration metric comprises a rate of change of a centripetalacceleration of said each piece of equipment along said longitudinalaxis.
 16. The system of claim 15, wherein said processor is furtherconfigured to partition said sequence of times into phases, wherein saidphases comprise a load phase ending when said centripetal accelerationchanges from positive to negative; an accelerate phase following saidload phase; a peak phase following said accelerate phase; and a transferphase following said peak phase and ending at an endpoint of said swing;said acceleration metric comprises an average rate of change of saidcentripetal acceleration during said accelerate phase.